hidden sl n symmetry in conformal field theories we prove that an irreducible representation of the virasoro algebra can be extracted from an irreducible representation space of thesl 2 current algebra by putting a constraint on the latter using the becchi rouet stora tyutin formalism thus there is asl 2 symmetry in the virasoro algebra but it is gauged and hidden this construction of the virasoro algebra is the quantum analogue of the hamiltonian reduction we then are naturally lead to consider a constrainedsl 2 wess zumino witten model this system is also related to quantum field theory of coadjoint orbit of the virasoro group based on this result we present a canonical derivation of thesl 2 current algebra in polyakov s theory of two dimensional gravity it is a manifestation of thesl 2 symmetry in conformal field theory hidden by the quantum hamiltonian reduction we also discuss the quantum hamiltonian reduction of thesl 2 current algebra and its relation to thew n algebra of zamolodchikov this makes it possible to define a natural generalization of the geometric action for thew n algebra despite its non lie algebraic nature

modularity of relatively rational vertex algebras and fusion rules of principal affine w algebras we study modularity of the characters of a vertex super algebra equipped with a family of conformal structures along the way we introduce the notions of rationality and cofiniteness relative to such a family we apply the results to determine modular transformations of trace functions on admissible modules over affine kac moody algebras and via brst reduction trace functions on minimal series representations of principal affine w algebras

conformal field theory and elliptic cohomology abstract in this paper we use conformal field theory to construct a generalized cohomology theory which has some properties of elliptic cohomology theory which was some properties of elliptic cohomology a part of our presentation is a rigorous definition of conformal field theory following segal s axioms and some examples such as lattice theories associated with a unimodular even lattice we also include certain examples and formulate conjectures on modular forms and monstrous moonshine related to the present work

a natural construction of borcherds fake baby monster lie algebra we use a z 2 orbifold of the vertex operator algebra associated to the niemeier lattice with root lattice a 8 3 and the no ghost theorem of string theory to construct a generalized kac moody algebra borcherds theory of automorphic products allows us to determine the simple roots and identify the algebra with the fake baby monster lie algebra

the kazhdan lusztig conjecture for w algebras the main result in this paper is the character formula for arbitrary irreducible highest weight modules of w algebras the key ingredient is the functor provided by quantum hamiltonian reduction which constructs the w algebras from affine kac moody km algebras and in a similar fashion w modules from km modules assuming certain properties of this functor the w characters are subsequently derived from the kazhdan lusztig conjecture for km algebras the result can be formulated in terms of a double coset of the weyl group of the km algebra the hasse diagrams give the embedding diagrams of the verma modules and the kazhdan lusztig polynomials give the multiplicities in the characters

geometry of w algebras from the affine lie algebra point of view to classify the classical field theories with w symmetry one has to classify the symplectic leaves of the corresponding w algebra which are the intersection of the defining constraint and the coadjoint orbit of the affine lie algebra if the w algebra in question is obtained by reducing a wess zumino novikov witten wznw model the fields that survive the reduction will obey nonlinear poisson bracket or commutator relations in general for example the toda models are well known theories which possess such a nonlinear w symmetry and many features of these models can only be understood if one investigates the reduction procedure in this paper we analyse the sl n case from which the so called wn algebras can be obtained one advantage of the reduction viewpoint is that it gives a constructive way to classify the symplectic leaves of the w algebra for the n 2 case corresponding to the coadjoint orbits of the virasoro algebra and for the n 3 case which gives rise to the zamolodchikov algebra our method in principle is capable of constructing explicit representatives on each leaf another attractive feature of this approach is the fact that the global nature of the w transformations can be explicitly described the reduction method also enables one to determine the classical highest weight hw states which are the stable minima of the energy on a w leaf these are important as only to those leaves can a hw representation space of the w algebra be associated which contains a classical hw state

compactications defined by arrangements ii locally symmetric varieties of type iv we define a new class of completions of locally symmetric varieties of type iv which interpolates between the baily borel compactification and mumford s toric compactifications an arithmetic arrangement in a locally symmetric variety of type iv determines such a completion canonically this completion admits a natural contraction that leaves the complement of the arrangement untouched the resulting completion of the arrangement complement is very much like a baily borel compactification it is the proj of an algebra of meromorphic automorphic forms when that complement has a moduli space interpretation then what we get is often a compactification obtained by means of geometric invariant theory we illustrate this with several examples moduli spaces of polarized k3 and enriques surfaces and the semi universal deformation of a triangle singularity we also discuss the question when a type iv arrangement is definable by an automorphic form

modular invariant representations of infinite dimensional lie algebras and superalgebras abstract in this paper we launch a program to describe and classify modular invariant representations of infinite dimensional lie algebras and superalgebras we prove a character formula for a large class of highest weight representations l of a kac moody algebra unk with a symmetrizable cartan matrix generalizing the weyl kac character formula kac v g 1974 funct anal appl 8 68 70 in the case of an affine unk this class includes modular invariant representations of arbitrary rational level m t u where t unk z and u unk n are relatively prime and m g g u g is the dual coxeter number we write the characters of these representations in terms of theta functions and calculate their asymptotics generalizing the results of kac and peterson kac v g peterson d h 1984 adv math 53 125 264 and of kac and wakimoto kac v g wakimoto m 1988 adv math 70 156 234 for the u 1 integrable case we work out in detail the case unk a1 1 in particular classifying all its modular invariant representations furthermore we show that the modular invariant representations of the virasoro algebra vir are precisely the minimal series of belavin et al belavin a a polyakov a m zamolodchikov a b 1984 nucl phys b 241 333 380 using the character formulas of feigin and fuchs feigin b l fuchs d b 1984 lect notes math 1060 230 245 we show that tensoring the basic representation and modular invariant representations of a1 1 produces all modular invariant representations of vir generalizing the results of goddard et al goddard p kent a olive d 1986 commun math phys 103 105 119 and of kac and wakimoto kac v g wakimoto m 1986 lect notes phys 261 345 371 in the unitary case we study the general branching functions as well all these results are generalized to the kac moody superalgebras introduced by kac kac v g 1978 adv math 30 85 136 and to n 1 super virasoro algebras we work out in detail the case of the superalgebra b 0 1 1 showing in particular that restricting to its even part produces again all modular invariant representations of vir these results lead to general conjectures about asymptotic behavior of positive energy representations and classification of modular invariant representations

a sub graph isomorphism algorithm for matching large graphs we present an algorithm for graph isomorphism and subgraph isomorphism suited for dealing with large graphs a first version of the algorithm has been presented in a previous paper where we examined its performance for the isomorphism of small and medium size graphs the algorithm is improved here to reduce its spatial complexity and to achieve a better performance on large graphs its features are analyzed in detail with special reference to time and memory requirements the results of a testing performed on a publicly available database of synthetically generated graphs and on graphs relative to a real application dealing with technical drawings are presented confirming the effectiveness of the approach especially when working with large graphs

the w n minimal model classification we first rigourously establish for any n 2 that the toroidal modular invariant partition functions for the not necessarily unitary w n p q minimal models biject onto a well defined subset of those of the su n su n wess zumino witten theories at level p n q n this permits considerable simplifications to the proof of the cappelli itzykson zuber classification of virasoro minimal models more important we obtain from this the complete classification of all modular invariants for the w 3 p q minimal models all should be realised by rational conformal field theories previously only those for the unitary models i e w 3 p p 1 were classified for all n our correspondence yields for free an extensive list of w n p q modular invariants the w 3 modular invariants like the virasoro minimal models all factorise into su 3 modular invariants but this fails in general for larger n we also classify the su 3 su 3 modular invariants and find there a new infinite series of exceptionals

generalized drinfeld sokolov reductions and kdv type hierarchies generalized drinfeld sokolov ds hierarchies are constructed through local reductions of hamiltonian flows generated by monodromy invariants on the dual of a loop algebra following earlier work of de groot et al reductions based upon graded regular elements of arbitrary heisenberg subalgebras are considered we show that in the case of the nontwisted loop algebra l gl n graded regular elements exist only in those heisenberg subalgebras which correspond either to the partitions ofn into the sum of equal numbersn pr or to equal numbers plus onen pr 1 we prove that the reduction belonging to the grade 1 regular elements in the casen pr yields thep p matrix version of the gelfand dickeyr kdv hierarchy generalizing the scalar casep 1 considered by ds the methods of ds are utilized throughout the analysis but formulating the reduction entirely within the hamiltonian framework provided by the classical r matrix approach leads to some simplifications even forp 1

quantum reduction for affine superalgebras we extend the homological method of quantization of generalized drinfeld sokolov reductions to affine superalgebras this leads in particular to a unified representation theory of superconformal algebras

stochastic navier stokes equations with caputo derivative driven by fractional noises abstract in this paper we consider the extended stochastic navier stokes equations with caputo derivative driven by fractional brownian motion we firstly derive the pathwise spatial and temporal regularity of the generalized ornstein uhlenbeck process then we discuss the existence uniqueness and holder regularity of mild solutions to the given problem under certain sufficient conditions which depend on the fractional order and hurst parameter h the results obtained in this study improve some results in existing literature

on uniqueness for some non lipschitz sde abstract we study the uniqueness in the path by path sense i e by of solutions to stochastic differential equations with additive noise and non lipschitz autonomous drift the notion of path by path solution involves considering a collection of ordinary differential equations and is in principle weaker than that of a strong solution since no adaptability condition is required we use results and ideas from the classical theory of ode s together with probabilistic tools like girsanov s theorem to establish the uniqueness property for some classes of noises including brownian motion and some drift functions not necessarily bounded nor continuous

z2 z2 codes and vertex operator algebras we construct a vertex operator algebra md using a code d in z2 z2 we also compute all the irreducible modules of md

almost harmonic maass forms and kac wakimoto characters we resolve a question of kac and explain the automorphic properties of char acters due to kac wakimoto pertaining to s mjn highest weight modules for n 1 we prove that the kac wakimoto characters are essentially holomorphic parts of certain general izations of harmonic weak maass forms which we call almost harmonic maass forms using a new approach this generalizes prior work of the first author and ono and the authors both of which treat only the case nd1 we also provide an explicit asymptotic expansion for the characters

semi infinite cohomology and string theory abstract we develop the theory of semi infinite cohomology of graded lie algebras first introduced by feigin we show that the relative semi infinite cohomology has a structure analogous to that of the de rham cohomology in kahler geometry we prove a vanishing theorem for a special class of modules and we apply our results to the case of the virasoro algebra and the fock module in this case the zero cohomology is identified as the physical subspace of the fock module and the no ghost theorem follows we reveal the profound relation of semi infinite cohomology theory to the gauge invariant free string theory constructed by banks and peskin we then indicate the connection between gauge invariant interacting string theories and the geometric realizations of the infinite dimensional lie algebras

one dimensional stochastic burgers equation driven by levy processes abstract in this paper we proved the global existence and uniqueness of the strong weak and mild solutions for one dimensional burgers equation perturbed by a poisson form process a poisson form and q wiener process with the dirichlet bounded condition we also proved the existence of the invariant measure of these models

affine kac moody algebras and semi infinite flag manifolds we study representations of affine kac moody algebras from a geometric point of view it is shown that wakimoto modules introduced in 18 which are important in conformal field theory correspond to certain sheaves on a semi infinite flag manifold with support on its schhubert cells this manifold is equipped with a remarkable semi infinite structure which is discussed in particular the semi infinite homology of this manifold is computed the cousin grothendieck resolution of an invertible sheaf on a semi infinite flag manifold gives a two sided resolution of an irreducible representation of an affine algebras consisting of wakimoto modules this is just the brst complex as a byproduct we compute the homology of an algebra of currents on the real line with values in a nilpotent lie algebra

white noise driven parabolic spdes with measurable drift abstract we prove existence and uniqueness of the solution of a white noise driven parabolic spde in case the drift is measurable and satisfies a one sided linear growth condition and the diffusion coefficient is nondegenerate has a locally lipschitz derivative and satisfies a linear growth condition the proof combines arguments similar to those of gyongy and pardoux together with an estimate of the density of the solution of the equation without drift which is obtained with the help of the malliavin calculus

automorphic forms fake monster algebras and hyperbolic reflection groups abstract we construct two families of automorphic forms related to twisted fake monster algebras and calculate their fourier expansions this gives a new proof of their denominator identities and shows that they define automorphic forms of singular weight we also obtain new infinite product identities which are the denominator identities of generalized kac moody superalgebras finally we describe the reflection groups of the root lattices of these algebras

efficient computation of isometry invariant distances between surfaces we present an efficient computational framework for isometry invariant comparison of smooth surfaces we formulate the gromov hausdorff distance as a multidimensional scaling like continuous optimization problem in order to construct an efficient optimization scheme we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples for isometry invariant comparison of surfaces in the case of partially missing data we present the partial embedding distance which is computed using a similar scheme the main idea is finding a minimum distortion mapping from one surface to another while considering only relevant geodesic distances we discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency

generalized burgers equations and euler painleve transcendents ii initial value problems for the generalized burgers equation gbe ut u betaux lambdaualpha delta 2 uxx are discussed for the single hump type of initial data both continuous and discontinuous the numerical solution is carried to the self similar intermediate asymptotic regime when the solution is given analytically by the self similar form the nonlinear transformed ordinary differential equations ode s describing the self similar form are generalizations of a class discussed by euler and painleva and quoted by kamke these ode s are new and it is postulated that they characterize gbe s in the same manner as the painlev equations categorize the kortweg de vries kdv type a connection problem for some related ode s satisfying proper asymptotic conditions at x infinity is solved the range of amplitude parameter is found for which the solution of the connection problem exists the other solutions of the above gbe which display several interesting features such as peaking breaking and a long shelf on the left for negative values of the damping coefficient lambda are also discussed the results are compared with those holding for the modified kdv equation with damping journal of mathematical physics is copyrighted by the american institute of physics

w algebras and chiral differential operators at the critical level abstract let a crit be the chiral algebra corresponding to the affine kac moody algebra at the critical level g crit let z crit be the center of a crit the commutative chiral algebra z crit admits a canonical deformation into a non commutative chiral algebra w in this paper we will express the resulting first order deformation via the chiral algebra d crit of chiral differential operators on g t at the critical level

the stochastic burgers equation we study burgers equation perturbed by a white noise in space and time we prove the existence of solutions by showing that the cole hopf transformation is meaningful also in the stochastic case the problem is thus reduced to the anaylsis of a linear equation with multiplicative half white noise an explicit solution of the latter is constructed through a generalized feynman kac formula typical properties of the trajectories are then discussed a technical result concerning the regularizing effect of the convolution with the heat kernel is proved for stochastic integrals

mathieu moonshine and symmetry surfing mathieu moonshine the observation that the fourier coefficients of the elliptic genus on k3 can be interpreted as dimensions of representations of the mathieu group has been proven abstractly but a conceptual understanding in terms of a representation of the mathieu group on the bps states is missing some time ago taormina and wendland showed that such an action can be naturally defined on the lowest non trivial bps states using the idea of symmetry surfing i e by combining the symmetries of different k3 sigma models in this paper we find non trivial evidence that this construction can be generalized to all bps states

structure of some categories of representations of infinite dimensional lie algebras the highest weight representations of a finite dimensional complex semisimple lie algebra 9 have been studied extensively and a number of interesting results have been obtained in the last few years an extensive bibliography is given in 7 in 2 3 a category cy of representations of g was introduced which turns out to be the proper setting for considering various questions regarding highest weight representations the aim of this paper is to extend the study of this notion to a kac moody algebra or more generally to a contragredient lie algebra g a corresponding to a square matrix a over c the study of such algebras was begun independently in 8 14 and subsequently a number of interesting results were proved these results show that many important properties from the finite dimensional setup i e from the context of 9 can be proved in the general setup involving g a in particular the notion of category was extended in 9 to the case of kac moody algebras and used in the proof of combinatorial identities

the monster lie algebra abstract we calculate the multiplicities of all the roots of the monster lie algebra this gives an example of a lie algebra all of whose simple roots and root multiplicities are known and which is not finite dimensional or an affine kac moody algebra there seem to be several similar infinite dimensional lie algebras which to a sympathetic eye appear to correspond to some of the sporadic simple groups

type ii codes even unimodular lattices and invariant rings we study self dual codes over the ring z sub 2k of the integers modulo 2k with relationships to even unimodular lattices modular forms and invariant rings of finite groups we introduce type ii codes over z sub 2k which are closely related to even unimodular lattices as a remarkable class of self dual codes and a generalization of binary type ii codes a construction of even unimodular lattices is given using type ii codes several examples of type ii codes are given in particular the first extremal type ii code over z sub 6 of length 24 is constructed which gives a new construction of the leech lattice the complete and symmetrized weight enumerators in genus g of codes over z sub 2k are introduced and the macwilliams identities for these weight enumerators are given we investigate the groups which fix these weight enumerators of type ii codes over z sub 2k and we give the molien series of the invariant rings of the groups for small cases we show that modular forms are constructed from complete and symmetrized weight enumerators of type ii codes shadow codes over z sub 2k are also introduced

how to determine the law of the solution to a stochastic partial differential equation driven by a levy space time noise we consider a stochastic partial differential equation on a lattice tx m2 x xp where is a space time levy noise a perturbative in the sense of formal power series strong solution is given by a tree expansion whereas the correlation functions of the solution are given by a perturbative expansion with coefficients that are represented as sums over a certain class of graphs called parisi wu graphs the perturbative expansion of the truncated connected correlation functions is obtained via a linked cluster theorem as sums over connected graphs only the moments of the stationary solution can be calculated as well in all these solutions the cumulants of the single site distribution of the noise enter as multiplicative constants to determine them e g by comparison with an empirical correlation function one can fit these constants e g by the methods of least squares and thereby one approximately determines laws of the solution and the driving noise

enriques surfaces analytic discriminants and borcherds s φ function in bor 96 borcherds constructed a non vanishing weight 4 modular form on the moduli space of marked polarized enriques surface of degree 2 by considering the twisted denominator function of the fake monster lie algebra associated to an automorphism of order 2 of the leech lattice fixing an 8 dimensional subspace in jt 94 and jt 96 we defined and studied a meromorphic multi valued modular form of weight 2 which we call the k3 analytic discriminant on the moduli space of marked polarized k3 surfaces of degree 2d in certain cases including when where p k are distinct primes our meromorphic form is actually a holomorphic form our construction involves a determinant of the laplacian on a polarized k3 surface with respect to the calabi yau metric together with the l 2 norm of the image of the period map with respect to a properly scaled holomorphic two form since the universal cover of any enriques surface is a k3 surface we can restrict the k3 analytic discriminant to the moduli space of degree 2 enriques surfaces the main result of this paper is the observation that the square of our degree 2 analytic discriminant viewed as a function on the moduli space of degree 2 enriques surfaces is equal to the borcherd s function up to a universal multiplicative constant this result generalizes known results in the study of generalized kac moody algebras and elliptic curves and suggests further connections with higher dimensional calabi yau varieties specifically those which can be realized as complete intersections in some possibly weighted projective space

on the cauchy problem for first order discontinuous ordinary differential equations abstract we prove the existence of extremal caratheodory solutions for the initial value problem x t f t x t for a e t 0 1 x 0 0 under weak conditions over f 0 1 r r

universal two parameter even spin w algebra abstract we construct the unique two parameter vertex algebra which is freely generated of type w 2 4 6 and generated by the weights 2 and 4 fields subject to some mild constraints all vertex algebras of type w 2 4 2 n for some n can be obtained as quotients of this universal algebra this includes the b and c type principal w algebras the z 2 orbifolds of the d type principal w algebras and many others which arise as cosets of affine vertex algebras inside larger structures as an application we classify all coincidences among the simple quotients of the b and c type principal w algebras as well as the z 2 orbifolds of the d type principal w algebras finally we use our classification to give new examples of principal w algebras of b c and d types which are lisse and rational

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

quantum reduction and representation theory of superconformal algebras abstract we study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction as an application we obtain in a unified way free field realizations and determinant formulas for all superconformal algebras

monstrous moonshine and monstrous lie superalgebras we prove conway and norton s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by frenkel lepowsky and meurman to do this we use the no ghost theorem from string theory to construct a family of generalized kac moody superalgebras of rank 2 which are closely related to the monster and several of the other sporadic simple groups the denominator formulas of these superalgebras imply relations between the thompson functions of elements of the monster i e the traces of elements of the monster on frenkel lepowsky and meurman s representation which are the replication formulas conjectured by conway and norton these replication formulas are strong enough to verify that the thompson functions have most of the moonshine properties conjectured by conway and norton and in particular they are modular functions of genus 0 we also construct a second family of kac moody superalgebras related to elements of conway s sporadic simple group col these superalgebras have even rank between 2 and 26 for example two of the lie algebras we get have ranks 26 and 18 and one of the superalgebras has rank 10 the denominator formulas of these algebras give some new infinite product identities in the same way that the denominator formulas of the a n n e kac moody algebras give the macdonald identities

traveling wave solutions u v to a generalized drinfel d sokolov system which satisfy u a1vm a0 abstract an analysis of the coupled generalized drinfel d sokolov equations u t 1 uu x 1 u xxx v x 0 and v t 2 uv x 2 v xxx 0 is performed in the case of traveling wave solutions u and v satisfying the condition u a 1 v m a 0 we are able to classify all such solutions in terms of the model parameters and we then discuss the planar dynamics of such solutions numerical solutions are obtained and discussed for a variety of parameter regimes such results are one possible generalization of those given by wu et al l wu s chen c pang traveling wave solutions for generalized drinfeld sokolov equations applied mathematical modeling 33 2009 4126 4130

matching 3 d models to 2 d images we consider the problem of analytically characterizing the set of all 2 d images that a group of 3 d features may produce and demonstrate that this is a useful thing to do our results apply for simple point features and point features with associated orientation vectors when we model projection as a 3 d to 2 d affine transformation we show how to represent the set of images that a group of 3 d points produces with two lines 1 d subspaces one in each of two orthogonal high dimensional spaces where a single image group corresponds to one point in each space the images of groups of oriented point features can be represented by a 2 d hyperbolic surface in a single high dimensional space the problem of matching an image to models is essentially reduced to the problem of matching a point to simple geometric structures moreover we show that these are the simplest and lowest dimensional representations possible for these cases we demonstrate the value of this way of approaching matching by applying our results to a variety of vision problems in particular we use this result to build a space efficient indexing system that performs 3 d to 2 d matching by table lookup this system is analytically built and accessed accounts for the effects of sensing error and is tested on real images we also derive new results concerning the existence of invariants and non accidental properties in this domain finally we show that oriented points present unexpected difficulties indexing requires fundamentally more space with oriented than with simple points we must use more images in a motion sequence to determine the affine structure of oriented points and the linear combinations result does not hold for oriented points

kazhdan lusztig conjecture for generalized kac moody algebras ii proof of the conjecture generalized kac moody algebras were introduced by borcherds in the study of conway and norton s moonshine conjectures for the monster sporadic simple group in this paper we prove the kazhdan lusztig conjecture for generalized kac moody algebras under a certain mild condition by using a generalization to the case of generalized kac moody algebras of jantzen s character sum formula our main formula generalizes the celebrated result for the case of kac moody algebras and describes the characters of irreducible highest weight modules over generalized kac moody algebras in terms of the extended kazhdan lusztig polynomials

fock representations and brst cohomology insl 2 current algebra we investigate the structure of the fock modules overa 1 1 introduced by wakimoto we show that irreducible highest weight modules arise as degree zero cohomology groups in a brst like complex of fock modules chiral primary fields are constructed as brst invariant operators acting on fock modules as a result we obtain a free field representation of correlation functions of thesu 2 wzw model on the plane and on the torus we also consider representations of fractional level arising in polyakov s 2d quantum gravity finally we give a geometrical borel weil like interpretation of the wakimoto construction

stochastic generalized burgers equations driven by fractional noises abstract the existence and uniqueness are proved for the solutions to a class of stochastic generalized burgers equations driven by multi parameter fractional noises in addition the existence and moment estimate are also obtained for the density of such a solution

the automorphism group of the 26 dimensional even unimodular lorentzian lattice abstract the group mentioned in the title is shown to be a certain infinitely generated coxeter group extended by the negative of the identity operation and the group of all automorphisms of the notorious leech lattice

decompositions of the moonshine module with respect to subvoas associated to codes over z2k abstract in this paper we give decompositions of the moonshine module v with respect to subvoas associated to extremal type ii codes over z 2 k for an integer k 2 those subvoas are isomorphic to the tensor product of 24 copies of the charge conjugation orbifold voa using such decompositions we obtain some elements of type 4 a k odd and 2 b k even of the monster simple group aut v

decomposition of the moonshine vertex operator algebra as virasoro modules abstract in this article we obtain a decomposition of the moonshine vertex operator algebra v associated with the algebra l 1 2 0 l 7 10 0 l 4 5 0 12 our method is based on a coset decomposition of the leech lattice associated with 2 a 2 12 using some codes in fact we construct a code vertex operator algebra mk c mt d with a ternary code d and a z 2 z 2 code c and use it to obtain a decomposition of v

feynman graph representation of the perturbation series for general functional measures abstract a representation of the perturbation series of a general functional measure is given in terms of generalized feynman graphs and rules the graphical calculus is applied to certain functional measures of levy type a graphical notion of wick ordering is introduced and is compared with orthogonal decompositions of the wiener ito segal type it is also shown that the linked cluster theorem for feynman graphs extends to generalized feynman graphs we perturbatively prove existence of the thermodynamic limit for the free energy density and the moment functions the results are applied to the gas of charged microscopic or mesoscopic particles neutral in average in d 2 dimensions generating a static field with quadratic energy density giving rise to a pair interaction the pressure function for this system is calculated up to fourth order we also discuss the subtraction of logarithmically divergent self energy terms for a gas of only one particle type by a local counterterm of first order

analytical solutions to a generalized drinfel d sokolov equation related to dssh and kdv6 abstract analytical solutions to the generalized drinfel d sokolov gds equations u t 1 uu x 1 u xxx v x 0 and v t 2 uv x 2 v xxx 0 are obtained for various values of the model parameters in particular we provide perturbation solutions to illustrate the strong influence of the parameters 1 and 2 on the behavior of the solutions we then consider a miura type transform which reduces the gds equations into a sixth order nonlinear differential equation under the assumption that 1 under such a transform the gds reduces to the sixth order drinfel d sokolov satsuma hirota dssh equation also known as kdv6 in the very special case 1 2 the method of homotopy analysis is applied in order to obtain analytical solutions to the resulting equation for arbitrary 1 and 2 an error analysis of the obtained approximate analytical solutions is provided

on the completeness of the set of classical w algebras obtained from ds reductions we clarify the notion of the ds generalized drinfeld sokolov reduction approach to classical cal w algebras we first strengthen an earlier theorem which showed that an sl 2 embedding cal s subset cal g can be associated to every ds reduction we then use the fact that a cal w algebra must have a quasi primary basis to derive severe restrictions on the possible reductions corresponding to a given sl 2 embedding in the known ds reductions found to date for which the cal w algebras are denoted by cal w s g algebras and are called canonical the quasi primary basis corresponds to the highest weights of the sl 2 here we find some examples of noncanonical ds reductions leading to cal w algebras which are direct products of cal w s g algebras and lq lq free field algebras with conformal weights delta in 0 1 over 2 1 we also show that if the conformal weights of the generators of a cal w algebra obtained from ds reduction are nonnegative delta geq 0 which is the case for all ds reductions known to date then the delta geq 3 over 2 subsectors of the weights are necessarily the same as in the corresponding cal w s g algebra these results are consistent with an earlier result by bowcock and watts on the spectra of cal w algebras derived by different means we are led to the conjecture that up to free fields the set of cal w algebras with nonnegative spectra delta geq 0 that may be obtained from ds reduction is exhausted by the canonical ones

segmentation registration and measurement of shape variation via image object shape a model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives metrics are described that compute an object representation s prior probability of local geometry by reflecting variabilities in the net s node and link parameter values and that compute a likelihood function measuring the degree of match of an image to that object representation a paradigm for image analysis of deforming such a model to optimize a posteriori probability is described and this paradigm is shown to be usable as a uniform approach for object definition object based registration between images of the same or different imaging modalities and measurement of shape variation of an abnormal anatomical object compared with a normal anatomical object examples of applications of these methods in radiotherapy surgery and psychiatry are given

on the role of the besov spaces for the solutions of the generalized burgers equation in homogeneous sobolev spaces abstract the generalized burgers equation tu xxu xuk 1 0 with initial data u0 in homogeneous sobolev spaces are investigated the starting point of this work is the construction of solutions in l 0 b 1 k for small size initial data in b 1 k if in addition the initial data belongs to l p s then the obtained solution is actually in l 0 l p s

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

fractional stochastic volterra equation perturbed by fractional brownian motion in this paper we consider a class of fractional stochastic volterra equation of convolution type driven by infinite dimensional fractional brownian motion with hurst index h 0 1 base on the explicit formula for the scalar resolvent function and the properties of the mittag leffler s function the existence and regularity results of the stochastic convolution process are established separate proofs are required for the cases of hurst parameter above and below 1 2 and it will turn out that the regularity of the solution increases with hurst parameter h

trigonometric and hyperbolic type solutions to a generalized drinfel d sokolov equation abstract a class of trigonometric and hyperbolic type solutions to the generalized drinfel d sokolov gds equations u t 1 uu x 1 u xxx v x 0 and v t 2 uv x 2 v xxx 0 is obtained for the case in which 2 0 for various values of the other model parameters the method of homotopy analysis is then applied to obtain local analytical solutions for nonzero values of the parameter 2 in effect extending the exact solutions we do not assume traveling wave solution forms for the analytical solutions that is we solve the generalized drinfel d sokolov equations as pdes without resorting to transforming the system to odes an error analysis of the obtained approximate local analytical solutions is provided then we outline a general framework by which one many construct solutions in either sine cosine or sinh cosh basis we provide the general perturbation expansion via homotopy analysis and we also discuss a method of selecting the convergence control parameter so as to minimize residual errors travelling solutions with time dependent amplitude are then discussed

binary codes and vertex operator super algebras abstract we study a vertex operator algebra whose virasoro element is a sum of pairwise orthogonal rational conformal vectors with central charge 1 2 the most important example is the moonshine modulev in particular we construct a series of vertex operator algebras whose full automorphism groups are finite namely we construct vertex operator algebrasmd i 0 md ifrom even linear binary coded z n2and prove that if the minimum weight ofdis greater than 2 then md 1 0 and the full automorphism group ofmdis finite from the viewpoint of finite group theory the construction of a vertex operator algebra has one advantage we can expect not only automorphisms ofd but also another one indeed ifdcontains a 8 4 4 hamming subcodec thencdefines a nontrivial involutive automorphism ofmd which is not induced from the automorphism group ofd in particular we have a finite group extension of aut d z n2 d

wakimoto modules opers and the center at the critical level abstract wakimoto modules are representations of affine kac moody algebras in fock modules over infinite dimensional heisenberg algebras in this paper we present the construction of the wakimoto modules from the point of view of the vertex algebra theory we then use wakimoto modules to identify the center of the completed universal enveloping algebra of an affine kac moody algebra at the critical level with the algebra of functions on the space of opers for the langlands dual group on the punctured disc giving another proof of the theorem of b feigin and the author

kac wakimoto characters and non holomorphic jacobi forms in this paper we investigate the automorphic properties of certain characters introduced by kac and wakimoto pertaining to s m n highest weight modules extending previous work of the first author and ono the first author and folsom and the second author we investigate the general case not specializing the jacobi variables we prove that the kac wakimoto characters are essentially holomorphic parts of multivariable mixed h harmonic maass jacobi forms which are certain non holomorphic generalizations of classical holomorphic jacobi forms this also gives extra structure to the previous considered cases

a class of vertex operator algebras constructed from z8 codes abstract in this paper we construct some vertex operator algebras using z 8 codes and some substructures of the lattice vertex operator algebra formula we also construct some modules using a notion of induced modules

on the stochastic burgers equation in the real line this is the publisher s version also available electronically from http projecteuclid org euclid aop 1022677386 abstract

characters and fusion rules for w algebras via quantized drinfeld sokolov reduction using the cohomological approach tow algebras we calculate characters and fusion coefficients for their representations obtained from modular invariant representations of affine algebras by the quantized drinfeld sokolov reduction

on a stochastic heat equation with first order fractional noises and applications to finance abstract in this paper we propose a class of stochastic heat equations with first order fractional noises we define a first order noise through the adjoint operator of the first order operator where the operation of the stochastic integral can be avoided in this framework the existence and uniqueness of the solution of the equation will be established further we give the regularity of the solution finally we model the term structure of forward rate with the solutions and give the conditions under which the market is arbitrary free

representations of vertex operator algebra v l for rank one lattice l we classify the irreducible modules for the fixed point vertex operator subalgebra v l of the vertex operator algebra v l associated to a positive definite even lattice of rank 1 under the automorphism lifted from the 1 isometry of l

object recognition through topo geometric shape models using error tolerant subgraph isomorphisms we propose a method for 3 d shape recognition based on inexact subgraph isomorphisms by extracting topological and geometric properties of a shape in the form of a shape model referred to as topo geometric shape model tgsm in a nutshell tgsm captures topological information through a rigid transformation invariant skeletal graph that is constructed in a morse theoretic framework with distance function as the morse function geometric information is then retained by analyzing the geometric profile as viewed through the distance function modeling the geometric profile through elastic yields a weighted skeletal representation which leads to a complete shape signature shape recognition is carried out through inexact subgraph isomorphisms by determining a sequence of graph edit operations on model graphs to establish subgraph isomorphisms with a test graph test graph is recognized as a shape that yields the largest subgraph isomorphism with minimal cost of edit operations in this paper we propose various cost assignments for graph edit operations for error correction that takes into account any shape variations arising from noise and measurement errors

lifts of automorphisms of vertex operator algebras in simple current extensions in this article we study isomorphisms between simple current extensions of a simple voa for example we classify the isomorphism classes of simple current extensions of the voas v sqrt2e 8 and v lambda 16 where 16 is the barnes wall lattice of rank 16 moreover we consider the same simple current extension and describe the normalizer of the abelian automorphism group associated with this extension in particular we regard the moonshine module v natural as simple current extensions of five subvoas v l for 2 elementary totally even lattices l and describe corresponding five normalizers of elementary abelian 2 group in the automorphism group of v natural in terms of v l by using this description we show that three of them form a monster amalgam

quantization and representation theory of finite w algebras in this paper we study the finitely generated algebras underlyingw algebras these so called finitew algebras are constructed as poisson reductions of kirillov poisson structures on simple lie algebras the inequivalent reductions are labeled by the inequivalent embeddings ofsl 2 into the simple lie algebra in question for arbitrary embeddings a coordinate free formula for the reduced poisson structure is derived we also prove that any finitew algebra can be embedded into the kirillov poisson algebra of a semi simple lie algebra generalized miura map furthermore it is shown that generalized finite toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finitew symmetry in the second part we brst quantize the finitew algebras the brst cohomology is calculated using a spectral sequence which is different from the one used by feigin and frenkel this allows us to quantize all finitew algebras in one stroke examples are given in the last part of the paper we study the representation theory of finitew algebras it is shown using a quantum version of the generalized miura transformation that the representations of finitew algebras can be constructed from the representations of a certain lie subalgebra of the original simple lie algebra as a byproduct of this we are able to construct the fock realizations of arbitrary finitew algebras

the 290 fixed point sublattices of the leech lattice abstract we determine the orbits of fixed point sublattices of the leech lattice with respect to the action of the conway group co 0 there are 290 such orbits detailed information about these lattices the corresponding coinvariant lattices and the stabilizing subgroups is tabulated in several tables

the arithmetic mirror symmetry and calabi yau manifolds we extend our variant of mirror symmetry for k3 surfaces gn3 and clarify its relation with mirror symmetry for calabi yau manifolds we introduce two classes for the models a and b of calabi yau manifolds fibrated by k3 surfaces with some special picard lattices these two classes are related with automorphic forms on iv type domains which we studied in our papers gn1 gn6 conjecturally these automorphic forms take part in the quantum intersection pairing for model a yukawa coupling for model b and mirror symmetry between these two classes of calabi yau manifolds recently there were several papers by physicists where it was shown on some examples we propose a problem of classification of introduced calabi yau manifolds our papers gn1 gn6 and n3 n14 give hope that this is possible they describe possible picard or transcendental lattices of general k3 fibers of the calabi yau manifolds

a note on free bosonic vertex algebra and its conformal vectors abstract we classify all the heisenberg and conformal vectors and we determine the full automorphism group of the free bosonic vertex algebra without gradation to describe it we introduce a notion of inner automorphisms of a vertex algebra

moonshine modules and a question of griess abstract we consider the situation in which a finite group acts on an infinite dimensional graded module in such a way that the graded trace functions are weakly holomorphic modular forms under a mild hypothesis we completely describe the asymptotic module structure of the homogeneous subspaces as a consequence we find that moonshine for a group gives rise to partial orderings on its irreducible representations this serves as a first answer to a question posed by griess in particular we show that our hypothesis holds for umbral moonshine and for automorphism groups of certain vertex operator algebras

on mathbb z _p z p orbifold constructions of the moonshine vertex operator algebra for p 3 5 7 13 we consider a mathbb z p orbifold construction of the moonshine vertex operator algebra v natural we show that the vertex operator algebra obtained by the mathbb z p orbifold construction on the leech lattice vertex operator algebra v lambda and a lift of a fixed point free isometry of order p is isomorphic to the moonshine vertex operator algebra v natural we also describe the relationship between those mathbb z p orbifold constructions and the mathbb z 2 orbifold construction in a uniform manner in appendix we give a characterization of the moonshine vertex operator algebra v natural by the existence of an orthogonal pair of ising vectors

generalized kac moody algebras on etudie une classe d algebres de lie qui ont une forme bilineaire contravariante qui est presque definie positive ces algebres generalisent celles de kac moody et peuvent etre considerees comme des algebres de kac moody avec des racines simples imaginaires

the relation between quantum w algebras and lie algebras by quantizing the generalized drinfeld sokolov reduction scheme for arbitrarysl2 embeddings we show that a large set open image in new window of quantumw algebras can be viewed as brst cohomologies of affine lie algebras the set open image in new window contains many knownw algebras such asw n andw 3 2 our formalism yields a completely algorithmic method for calculating thew algebra generators and their operator product expansions replacing the cumbersome construction ofw algebras as commutants of screening operators by generalizing and quantizing the miura transformation we show that anyw algebra in open image in new window can be embedded into the universal enveloping algebra of a semisimple affine lie algebra which is up to shifts in level isomorphic to a subalgebra of the original affine algebra thereforeany realization of this semisimple affine lie algebra leads to a realization of thew algebra in particular one obtains in this way a general and explicit method for constructing the free field realizations and fock resolusions for all algebras in open image in new window some examples are explicitly worked out

weyl kac type character formula for admissible representations of borcherds kac moody lie superalgebras we prove that borcherds kac moody lie superalgebras yield weyl kac type character formulas for some specific types of admissible representations our results generalize the results of kac and wakimoto proc natl acad sci usa 85 4956 4960 1988 by extending the weyl kac character formula for integrable irreducible highest weight modules over kac moody algebras to the case of admissible irreducible highest weight modules over borcherds kac moody lie superalgebras