fock space representations of affine lie algebras and integral representations in the wess zumino witten models fock space representations of affine lie algebras are studied explicit forms of correction terms adding to the currentsf i z are determined it is proved that the sugawara energy momentum tensor on the fock spaces is quadratic in free bosons furthermore screening operators are constructed this implies the existence of generalized hypergeometric integrals satisfying the knizhnik zamolodchikov equation

a q deformation of wakimoto modules primary fields and screening operators theq vertex operators of frenkel and reshetikhin are studied by means of aq deformation of the wakimoto module for the quantum affine algebrau q widehat mathfrak s mathfrak l 2 at an arbitrary levelk 0 2 a fock module version of theq deformed primary field of spinj is introduced as well as the screening operators which anti commute with the action ofu q widehat mathfrak s mathfrak l 2 up to a total difference of a field a proof of the intertwining property is given for theq vertex operators corresponding to the primary fields of spinj 1 2z 0 a sample calculation of the correlation function is also given

on the probability of staying above a wall for the 2 1 dimensional sos model at low temperature we obtain sharp asymptotics for the probability that the 2 1 dimensional discrete sos interface at low temperature is positive in a large region for a square region lambda both under the infinite volume measure and under the measure with zero boundary conditions around lambda this probability turns out to behave like exp tau beta 0 l log l with tau beta 0 the surface tension at zero tilt also called step free energy and l the box side this behavior is qualitatively different from the one found for continuous height massless gradient interface models bolthausen et al commun math phys 170 2 417 443 1995 deuschel et al stochastic process appl 89 2 333 354 2000

modules over the algebra vir a b abstract for any two complex numbers a and b v i r a b is a central extension of w a b which is universal in the case a b 0 1 where w a b is the lie algebra with basis l n w n n z and relations l m l n n m l m n l m w n a n b m w m n w m w n 0 in this paper we construct and classify a class of non weight modules over the algebra v i r a b which are free u c l 0 c w 0 modules of rank 1 it is proved that such modules can only exist for a z

generalized verma modules over sln 2 induced from u hn free sln 1 modules abstract a class of generalized verma modules over sl n 2 are constructed from sl n 1 modules which are u h n free modules of rank 1 the necessary and sufficient conditions for these sl n 2 modules to be simple are determined this leads to a class of new simple sl n 2 modules

on osp 2 2 conformal field theories we study the conformal field theories corresponding to current superalgebras osp 2 2 1 k and osp 2 2 2 k we construct the free field realizations screen currents and primary fields of these current superalgebras at general level k all the results for osp 2 2 2 k are new and the results for the primary fields of osp 2 2 1 k also seem to be new our results are expected to be useful in the supersymmetric approach to gaussian disordered systems such as the random bond ising model and the dirac model

non weight modules over the affine virasoro algebra of type a1 in this paper we study a class of nonweight modules over the affine virasoro algebra of type a1 which are free modules of rank one when restricted to the universal enveloping algebra of the cartan subalgebra modulo center we give the classification of such modules moreover the simplicity and the isomorphism classes of these modules are determined in this paper we study a class of nonweight modules over the affine virasoro algebra of type a1 which are free modules of rank one when restricted to the universal enveloping algebra of the cartan subalgebra modulo center we give the classification of such modules moreover the simplicity and the isomorphism classes of these modules are determined

irreducible modules over finite simple lie conformal superalgebras of type k we construct all finite irreducible modules over lie conformal superalgebras of type k we construct all finite irreducible modules over lie conformal superalgebras of type k

irreducible witt modules from weyl modules and gln modules abstract for an irreducible module p over the weyl algebra k n resp k n and an irreducible module m over the general linear lie algebra gl n using shen s monomorphism we make p m into a module over the witt algebra w n resp over w n we obtain the necessary and sufficient conditions for p m to be an irreducible module over w n resp w n and determine all submodules of p m when it is reducible thus we have constructed a large family of irreducible weight modules with many different weight supports and many irreducible non weight modules over w n and w n including some known modules and many new modules

minimal positive stencils in meshfree finite difference methods for the poisson equation meshfree finite difference methods for the poisson equation approximate the laplace operator on a point cloud desirable are positive stencils i e all neighbor entries are of the same sign classical least squares approaches yield large stencils that are in general not positive we present an approach that yields stencils of minimal size which are positive we provide conditions on the point cloud geometry so that positive stencils always exist the new discretization method is compared to least squares approaches in terms of accuracy and computational performance

a new family of modules over the virasoro algebra abstract in this paper we constructed a new family of virasoro modules h parameterized by complex numbers 0 c and a polynomial h t they are a special type of modules on which the non central cartan part acts freely of infinite rank these modules are natural generalizations of the modules defined and studied in 5 11 and 19 we determine the sufficient and necessary conditions for them to be irreducible when they are reducible we also determine all their maximal submodules and corresponding simple quotients explicitly for some special cases we can determine all submodules

new representations of affine kac moody algebras abstract let h be a cartan subalgebra of an affine kac moody algebra without containing the center in this paper we classify the module structures on u h for all affine kac moody algebras which are free u h modules of rank 1 these modules exist only for type a l 1 l 1 or c l 1 l 2 affine kac moody algebras they are generically non weight and simple hence we obtain a class of new simple modules over these affine kac moody algebras

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

random walks in cones we study the asymptotic behavior of a multidimensional random walk in a general cone we find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone the main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments for the proof of tail asymptotics and integral limit theorems we use a strong approximation of random walks by brownian motion for the proof of local limit theorems we suggest a rather simple approach which combines integral theorems for random walks in cones with classical local theorems for unrestricted random walks we also discuss some possible applications of our results to ordered random walks and lattice path enumeration

a family of non weight modules over the super virasoro algebras abstract in this paper a family of non weight modules over the super virasoro algebras are constructed these modules over the ramond algebra are free of rank 1 when restricted as modules over the cartan subalgebra h while these modules over the neveu schwarz algebra are free of rank 2 when restricted as modules over the cartan subalgebra h we obtain a sufficient and necessary condition for such modules to be simple moreover we determine the isomorphism classes of these modules finally we show that these modules constitute a complete classification of free u h modules of rank 1 over the super virasoro algebra of ramond type and also constitute a complete classification of free u h modules of rank 2 over the super virasoro algebra of neveu schwarz type

irreducible virasoro modules from irreducible weyl modules abstract we use block s results to classify irreducible modules over the differential operator algebra c t t 1 d d t from modules a over c t t 1 d d t and using the twisting technique we construct a class of modules a b over the virasoro algebra for any b c these new virasoro modules are generally not weight modules the necessary and sufficient conditions for a b to be irreducible are obtained then we determine the necessary and sufficient conditions for two such irreducible virasoro modules to be isomorphic many interesting examples for such irreducible virasoro modules with different features are provided at the end of the paper in particular the class of irreducible virasoro modules b for any c and any b c are defined on the polynomial algebra c x

on the ill conditioning in the new higher order multipoint method the new higher order approximation multipoint technique in the meshless fdm is considered the method following the original collatz multipoint concept is based on arbitrary irregular meshes moving weighted least squares approximation and the global local or global local formulations of boundary value problems two basic versions of the multipoint meshless fd approach are developed the general and the specific ones unfortunately ill conditioning phenomenon may be encountered when the general multipoint approach is considered therefore several modifications of the multipoint algorithm have been proposed and tested to avoid this problem a variety of tests done show that the proposed concepts work well however efficiency problem in some versions which involves additional calculations is the main issue now alternatively the simplest solution in this situation is to use a regularization term in the weighted error functional numerical results demonstrate the effectiveness of the proposed versions in situation when ill conditioning or singularity could be encountered

fraction representations and highest weight like representations of the virasoro algebra abstract in this paper two new classes of irreducible modules over the centerless virasoro algebra v are obtained these modules are generally not weight modules or whittaker modules we first construct a class of modules over v parameterized by any 2 n 2 complex numbers for any nonnegative integer n which we call fraction modules the necessary and sufficient conditions for fraction modules to be irreducible are determined also we determine the necessary and sufficient conditions for two irreducible fraction modules to be isomorphic then we define highest weight like verma modules over v these modules behave like highest weight verma modules it is proved that each highest weight like verma module has an irreducible quotient module which is isomorphic to a subquotient of some reducible fraction module

entropic repulsion of an interface in an external field we consider an interface above an attractive hard wall in the complete wetting regime and submitted to the action of an external increasing convex potential and study its delocalization as the intensity of this potential vanishes our main motivation is the analysis of critical prewetting which corresponds to the choice of a linear external potential we also present partial results on critical prewetting in the two dimensional ising model as well as a few weak results on pathwise estimates for the pure wetting problem for effective interface models

bosonic fock representations of the affine virasoro algebra bosonic fock representations of the virasoro algebra and the affine lie algebras attached to classical lie algebras with non zero centres are explicitly presented based on these fock representations of the affine virasoro algebra are constructed an automorphism of the affine virasoro algebra is also given

simple modifications for stabilization of the finite point method a stabilized version of the finite point method fpm is presented a source of instability due to the evaluation of the base function using a least square procedure is discussed a suitable mapping is proposed and employed to eliminate the ill conditioning effect due to directional arrangement of the points a step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution it is shown that the conventional version of fpm may lead to wrong results when the proposed mapping algorithm is not used it is shown that another source for instability and non monotonic convergence rate in collocation methods lies in the treatment of neumann boundary conditions unlike the conventional fpm in this work the neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods the stabilization procedure may be considered as an interpretation of the finite calculus fic method the main difference between the two stabilization procedures lies in choosing the characteristic length in fic and the weight of the boundary residual in the proposed method the new approach also provides a unique definition for the sign of the stabilization terms the reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared several numerical examples are presented to demonstrate the performance and convergence of the proposed methods copyright 2005 john wiley sons ltd

fock representations of the affine lie algebra a 1 1 the aim of this note is to show that the affine lie algebraa1 1 has a natural family v of fock representations on the spacec xi yj i andj parametrized by v c2 by corresponding the highest weight of to each the parameter spacec2 forms a double cover of the weight spacec 0 c 1 with singularities at linear forms of level 2 this number is 1 times the dual coxeter number our results contain explicit realizations of irreducible non integrable highest wieghta1 1 modules for generic v

finite conformal modules over n 2 3 4 superconformal algebras in this paper we continue the study of representation theory of formal distribution lie superalgebras initiated by cheng and kac asian j math 1 181 193 1997 2 153 156 1998 erratum we study finite verma type conformal modules over the n 2 n 3 and the two n 4 superconformal algebras and also find explicitly all singular vectors in these modules from our analysis of these modules we obtain a complete list of finite irreducible conformal modules over the n 2 n 3 and the two n 4 superconformal algebras

construction of simple non weight sl 2 modules of arbitrary rank abstract we study simple non weight sl 2 modules which are finitely generated as c z modules we show that they are described in terms of semilinear endomorphisms and prove that the smith type induces a stratification on the set of these sl 2 modules providing thus new invariants moreover we show that there is a notion of duality for these type of sl 2 modules finally we show that there are simple non weight sl 2 modules of arbitrary rank by constructing a whole new family of them

simple sl_ n 1 module structures on u h abstract we study the category m consisting of u sl n 1 modules whose restriction to u h is free of rank 1 in particular we classify isomorphism classes of objects in m and determine their submodule structure this leads to new sl n 1 modules for n 1 we also find the central characters and derive an explicit formula for taking tensor product with a simple finite dimensional module

jackson integrals of jordan pochhammer type and quantum knizhnik zamolodchikov equations we show that theq difference systems satisfied by jackson integrals of jordan pochhammer type give a class of the quantum knizhnik zamolodchikov equation for u q widehat mathfrak s mathfrak l 2 in the sense of frenkel and reshetikhin

confluent primary fields in the conformal field theory for any complex simple lie algebra we generalize the primary fields in the wess zumino novikov witten conformal field theory for a case with irregular singularities we refer to these generalized primary fields as confluent primary fields we present the screening currents ward identity a recursion rule for computing the expectation values of the products of confluent primary fields in the case of the expectation values of the products of confluent primary fields are integral formulas of solutions to confluent knizhnik zamolodchikov kz equations given in jimbo et al 2008 j phys a math theor 41 175205 by computing the operator product expansion of the energy momentum tensor t z and the confluent primary fields we obtain new differential operators moreover in the case of these differential operators are the same as those of the confluent kz equations jimbo et al 2008

a new n 6 superconformal algebra in this paper we construct a newn 6 superconformal algebra which extends the virasoro algebra by theso 6 current algebra by 6 odd primary fields of conformal weight 3 2 and by 10 odd primary fields of conformal weight 1 2 the commutation relations of this algebra which we will refer to asck 6 are represented by short distance operator product expansions ope we constructck 6 as a subalgebra of theso 6 superconformal algebra k6 thus giving it a natural representation as first order differential operators on the circle withn 6 extended symmetry we show thatck 6 has no nontrivial central extensions

irreducible virasoro modules from tensor products ii abstract in this paper we obtain a class of virasoro modules by taking tensor products of a finite number of irreducible virasoro modules of the form i a i defined in 19 with irreducible highest weight modules v h or with irreducible virasoro modules ind n defined in 24 i e the tensor product i 1 m i a i v where v is v h or ind n we obtain the necessary and sufficient conditions for such tensor product modules to be irreducible and determine the necessary and sufficient conditions for two of them to be isomorphic we compare the tensor products with other known irreducible non weight virasoro modules we also characterize these irreducible tensor products

space time meshfree collocation method methodology and application to initial boundary value problems a novel space time meshfree collocation method stmcm for solving systems of non linear ordinary and partial differential equations by a consistent discretization in both space and time is proposed as an alternative to established mesh based methods the stmcm belongs to the class of truly meshfree methods i e the methods that do not have any underlying mesh but work on a set of nodes only without any a priori node to node connectivity instead the neighbouring information is established on the fly the stmcm is constructed using the interpolating moving least squares technique which allows a simplified implementation of boundary conditions due to fulfillment of the kronecker delta property by the kernel functions which is not the case for the major part of other meshfree methods the method is validated by several examples ranging from interpolation problems to the solution of pdes whereas the stmcm solutions are compared with either analytical or reference ones

positivity conditions in meshless collocation methods collocation meshless methods are conceptually simple easy to implement and fast numerical methods the robustness of collocation methods has however been an issue especially for scattered set of points in this paper we show that the robustness of collocation meshless methods can be improved by ensuring that certain conditions defined as the positivity conditions are satisfied when constructing approximation functions and their derivatives the significance of positivity conditions is pointed out by an error analysis of the finite cloud method which is a collocation based meshless method we propose techniques based on modification of weighting functions to ensure satisfaction of positivity conditions on the approximation function and its derivatives when using a scattered set of points several types of weighting functions are tested for 1d and 2d problems on scattered points numerical results demonstrate the effectiveness of collocation methods when positivity conditions are satisfied

quantum algebra structure of certain jackson integrals theq difference system satisfied by jackson integrals with a configuration ofa type root system is studied we explicitly construct some linear combination of jackson integrals which satisfies the quantum knizhnik zamolodchikov equation for the 2 point correlation function ofq vertex operators introduced by frenkel and reshetikhin for the quantum affine algebra u q widehat mathfrak s mathfrak l 2 the expression of integrands for then point case is conjectured and a set of linear relations for the corresponding jackson integrals is proved

meshfree finite difference approximations for functions of the eigenvalues of the hessian we introduce meshfree finite difference methods for approximating nonlinear elliptic operators that depend on second directional derivatives or the eigenvalues of the hessian approximations are defined on unstructured point clouds which allows for very complicated domains and a non uniform distribution of discretisation points the schemes are monotone which ensures that they converge to the viscosity solution of the underlying pde as long as the equation has a comparison principle numerical experiments demonstrate convergence for a variety of equations including problems posed on random point clouds complex domains degenerate equations and singular solutions

on self similar lie algebras and virtual endomorphisms we introduce the notion of virtual endomorphisms of lie algebras and use it as an approach for constructing self similarity of lie algebras this is done in particular for a class of metabelian lie algebras having homological type fp n which are lie algebra analogues of lamplighter groups we establish several criteria when the existence of virtual endomorphism implies a self similar lie structure furthermore we prove that the classical lie algebra sl n k where char k does not divide n affords non trivial faithful self similarity

an application of aomoto gelfand hypergeometric functions to the su n knizhnik zamolodchikov equation solutions to the knizhnik zamolodchikov equation for verma modules of the lie algebra mathfrak s mathfrak l n 1 mathbb c are explicitly given by certain integrals called aomoto gelfand hypergeometric functions

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

an invariance principle to ferrari spohn diffusions we prove an invariance principle for a class of tilted 1 1 dimensional sos models or equivalently for a class of tilted random walk bridges in mathbb z the limiting objects are stationary reversible ergodic diffusions with drifts given by the logarithmic derivatives of the ground states of associated singular sturm liouville operators in the case of a linear area tilt we recover the ferrari spohn diffusion with log airy drift which was derived in ferrari and spohn ann probab 33 4 1302 1325 2005 in the context of brownian motions conditioned to stay above circular and parabolic barriers

level 1 wzw superselection sectors the superselection structure of the wess zumino witten theory based on the affine lie algebra widehat so n at level one is investigated for arbitraryn by making use of the free fermion representation of the affine algebra the endomorphisms which represent the superselection sectors on the observable algebra can be constructed as endomorphisms of the underlying majorana algebra these endomorphisms do not close on the chiral algebra of the theory but we are able to obtain a larger algebra on which the endomorphisms close the composition of equivalence classes of the endomorphisms reproduces the wzw fusion rules

superconformal algebras and transitive group actions on quadrics a classification of physical superconformal algebras is given the list consists of seven algebras the virasoro algebra the neveu schwarz algebra then 2 3 and 4 algebras the superalgebra of all vector fields on then 2 supercircle and a new algebrack6 constructed in 3 the proof relies heavily on the classification of all connected subgroups ofson c which act transitively on the quadric v v 1

a class of simple weight virasoro modules abstract for a simple module m over the positive part of the virasoro algebra actually for any simple module over some finite dimensional solvable lie algebras a r and any c a class of weight modules n m over the virasoro algebra is constructed these weight modules have infinite dimensional weight spaces if dim m 1 the necessary and sufficient conditions for n m to be simple are obtained we also determine the necessary and sufficient conditions for two such irreducible virasoro modules to be isomorphic many examples for such irreducible virasoro modules with different features are provided in particular the irreducible weight virasoro modules 1 2 1 2 are defined on the polynomial algebra c x c t t 1 for any 1 2 1 2 c with 1 or 2 nonzero by twisting the weight modules n m we also obtain nonweight simple virasoro modules n m for any nonconstant c t t 1

on some convergence results for fdm with irregular mesh abstract the proof of convergence of the finite difference method with arbitrary irregular meshes for some class of elliptic problems is presented by the use of the truncation error technique and stability analysis it was showed that max i u i u h i ch i e the solution u h converges linearly with the size of the star correctness of this theorem was also confirmed by numerical tests

on the derivation of highest order compact finite difference schemes for the one and two dimensional poisson equation with dirichlet boundary conditions the primary aim of this paper is to answer the question what are the highest order five or nine point compact finite difference schemes to answer this question we present several simple derivations of finite difference schemes for the one and two dimensional poisson equation on uniform quasi uniform and nonuniform face to face hyperrectangular grids and directly prove the existence or nonexistence of their highest order local accuracies our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights for the one dimensional problem the derivation using the three point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high order local accuracy however for the two dimensional problem the derivation using the corresponding five point stencil on uniform and quasi uniform grids yields a scheme with at most second order local accuracy and on nonuniform grids yields at most first order local accuracy when expanding the five poin

leibniz algebras of heisenberg type we introduce and provide a classification theorem for the cl ass of heisenberg fock leibniz algebras this category of algebras is formed by those leibniz algebras l whose corresponding lie algebras are heisenberg algebras hn and whose hn modules i where i denotes the ideal generated by the squares of elements of l are isomorphic to fock modules we also consider the three dimensional heisenberg algebra h3 and study three classes of leibniz algebras with h3 as corresponding lie algebra by taking certain generalizations of the fock module moreover we describe the class of leibniz algebras with hn as corresponding lie algebra and such that the action i hn i gives rise to a minimal faithful representation of hn the classification of this family of leibniz algebras for the case of n 3 is given ams subject classifications 2010 17a32 17b30 17b10

twisted wess zumino witten models on elliptic curves investigated is a variant of the wess zumino witten model called a twisted wzw model which is associated to a certain lie group bundle on a family of elliptic curves the lie group bundle is a non trivial bundle with flat connection and related to the classical elliptic r matrix the usual non twisted wzw model is associated to a trivial group bundle with trivial connection on a family of compact riemann surfaces and a family of its principal bundles the twisted wzw model on a fixed elliptic curve at the critical level describes the xyz gaudin model the elliptic knizhnik zamolodchikov equations associated to the classical elliptic r matrix appear as flat connections on the sheaves of conformal blocks in the twisted wzw model

wakimoto realizations of current algebras an explicit construction a generalized wakimoto realization of can be associated with each parabolic subalgebra of a simple lie algebra according to an earlier proposal by feigin and frenkel in this paper the proposal is made explicit by developing the construction of wakimoto realizations from a simple but unconventional viewpoint an explicit formula is derived for the wakimoto current first at the poisson bracket level by hamiltonian symmetry reduction of the wznw model the quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate by means of commutators the affine sugawara stress energy tensor is verified to have the expected quadratic form in the constituents which are symplectic bosons belonging to and a current belonging to the quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold the effect of this choice is investigated in detail by constructing quantum coordinate transformations finally the explicit form of the screening charges for each generalized wakimoto realization is determined and some applications are briefly discussed

representations of the lie algebra of derivations for quantum torus abstract let der c q be the derivation lie algebra of the quantum torus c q we construct a functor from gld modules to der c q modules which generalizes the constructions obtained by shen scientia sinica a 29 1986 570 larsson internat j modern phys a 7 1992 6493 and rao j algebra 182 1996 401 we also give a complete description of the structure of the der c q modules when all the entries of the quantum torus matrix q qij d d are roots of unity

quantum group structure in the fock space resolutions of widehat sl n representations we describe a complex of wakimoto type fock space modules for the affine kac moody algebra widehat sl n the intertwining operators that build the complex are obtained from contour integrals of so called screening operators we show that a quantum group structure underlies the algebra of screening operators this observation greatly facilitates the explicit determination of the intertwiners we conjecture that the complex provides a resolution of an irreducible highest weight module in terms of fock spaces

lie algebra modules with finite dimensional weight spaces i let g denote a reductive lie algebra over an algebraically closed field of characteristic zero and let 4 denote a cartan subalgebra of g in this paper we study finitely generated g modules that decompose into direct sums of finite dimensional 4 weight spaces we show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of irreducible modules those we call torsion free modules we also show that if g is a simple lie algebra that admits a torsion free module then g is of type a or c

quasifinite representations of a lie algebra of block type abstract let b be the lie algebra of block type over c with basis l i c i z i 1 and relations l i l j i 1 j 1 l i j 0 i j 2c c l i 0 in this paper it is proved that a quasifinite irreducible b module is a highest or lowest weight module furthermore the quasifinite irreducible highest weight modules are classified and the unitary ones are proved to be trivial

wess zumino witten model on elliptic curves at the critical level we construct a gaudin type lattice model as the wess zumino witten model on elliptic curves at the critical level bethe eigenvectors are obtained by the bosonization technique

wn and wn module structures on u hn abstract let h n be the cartan subalgebra of the witt algebras w n der c t 1 t 2 t n and w n der c t 1 1 t 2 1 t n 1 where 1 n in this paper we classify the modules over w n and over w n which are free u h n modules of rank 1 these are the w n modules n a s for some n 1 n c n a c and s 1 2 n and w n modules n a for some n c n and some a c

constrained brownian motion fluctuations away from circular and parabolic barriers motivated by the polynuclear growth model we consider a brownian bridge b t with b t 0 conditioned to stay above the semicircle ct t p t 2 t2 in the limit of large t the fluctuation scale of b t ct t is t 1 3 and its time correlation scale is t 2 3 we prove that in the sense of weak convergence of path measures the conditioned brownian bridge when properly rescaled converges to a stationary diffusion process with a drift explicitly given in terms of airy functions the dependence on the reference point t t 2 1 1 is only through the second derivative of ct t at t t we also prove a corresponding result where instead of the semicircle the barrier is a parabola of height t 1 2 the fluctuation scale is then t 2 3 more general conditioning shapes are briefly discussed 1 introduction and main results we consider the brownian bridge b t over the time interval t t t 0 b t b t 0 conditioned to lie above the semicircle ct t t 2 t 2 let b t be the conditioned brownian bridge and let xt t b t ct t be the deviation of b t away from ct t see figure 1 clearly xt t 0 xt t xt t 0 and the path measure of the process is defined on c t t r c t t the space of continuous functions over the interval t t equipped with the supremum norm the issue is to understand the statistical properties of xt t for large t a well studied special case is when ct t is replaced by the function zero the brownian bridge is then constrained to stay positive a stochastic process known as brownian excursion in the limit of large t it converges to the three dimensional bessel process time dependent barriers like the circle seem to be hardly studied an exception is the parabola gt 2 t t 2 t 2 for

a meshless method with conforming and nonconforming sub domains summary an accurate and easy integration technique is desired for the meshless methods of weak form as is well known a sub domain method is often used in computational mechanics the conforming sub domains where the sub domains are not separated nor overlapped each other are often used while the nonconforming sub domains could be employed if needed in the latter cases the integrations of the sub domains may be performed easily by choosing a simple configuration and then the meshless method with nonconforming sub domains is considered one of the reasonable choices for computational mechanics without the troublesome integration in this paper we propose a new sub domain meshless method it is noted that because the method can employ both the conforming and the nonconforming sub domains the integration for the weak form is necessarily accurate and easy by selecting the nonconforming sub domains with simple configuration the boundary value problems including the poisson s equation and the helmholtz s equation are analyzed by using the proposed method the numerical solutions are compared with the exact solutions and the solutions of the collocation method showing that the relative errors by using the proposed method are smaller than those by using the collocation method and that the proposed method possesses a good convergence copyright 2016 john wiley sons ltd

dyson ferrari spohn diffusions and ordered walks under area tilts we consider families of non colliding random walks above a hard wall which are subject to a self potential of tilted area type we view such ensembles as effective models for the level lines of a class of 2 1 dimensional discrete height random surfaces in statistical mechanics we prove that under rather general assumptions on the step distribution and on the self potential such walks converge under appropriate rescaling to non intersecting ferrari spohn diffusions associated with limiting sturm liouville operators in particular the limiting invariant measures are given by the squares of the corresponding slater determinants

a class of new simple modules for sln 1 and the witt algebra abstract let g sl n 1 w n or w n d i 1 n c t i in this paper we classify the full subcategory d g of g mod consisting of modules which are free of rank 1 when restricted to u d the irreducibility of modules in d g is determined using modules in d sl n 1 we construct classes of modules which are free of finite rank and classes of infinitely generated modules when restricted to the cartan subalgebra

on an h type mesh refinement strategy based on minimization of interpolation errors abstract an adaptive finite element method is proposed which involves an automatic mesh refinement in areas of the mesh where local errors are determined to exceed a pre assigned limit the estimation of local errors is based on interpolation error bounds and extraction formulas for highly accurate estimates of second derivatives applications to several two dimensional model problems are discussed the results indicate that the method can be very effective for both regular problems and problems with strong singularities

consistency conditions for the influence graphs generalized finite difference method the modeling of physical phenomena is most often conveyed through partial differential equations governing continuous fields computational approaches are used afterwards in order to approximate the solutions to these equations in doing so a discretized version of the initial model must be set up using one of the numerous available methods this paper illustrates how influence graphs weighted digraphs with geometrical attributes may behave in the same way as differential operators in so far as a set of appropriate conditions of consistency are satisfied these conditions are written explicitly for the most often used cases including differential boundary operators on the one hand a consistent neighborhood may be regarded as a generalization of a classical finite difference scheme on the other hand a consistent influence graph is a discrete object modeling a physical behavior as well as its continuous counterpart numerical experimentations address firstly the second order diffusion model and lastly the fourth order kirchhoff theory of plate deflection

realization of the space of conformal blocks in lie algebra modules abstract using integrable irreducible representations of generalized twisted affine lie algebra modules we give a realization of the space of conformal blocks of conformal field theory on a stable algebraic curve many basic properties of the conformal blocks such as finite dimensionality of the space invariance of the conformal blocks under suitable formal neighborhood changes and the property of propagation of vacua are discussed finally a relative local 1 form around a fixed point of the order two automorphism of the curve is given

classification of finite irreducible conformal modules over lie conformal superalgebras of block type abstract we introduce a class of infinite lie conformal superalgebras s p of block type and classify their finite irreducible conformal modules for any nonzero parameter p in particular we show that such a conformal module admits a nontrivial extension of a finite conformal module over ns if p 1 where ns is a neveu schwarz conformal subalgebra of s p as a byproduct we also obtain the classification of finite irreducible conformal modules over a series of finite lie conformal superalgebras s n for n 1

irreducible representations of _ with a 1 dimensional weight space in this paper we classify all irreducible linear representations of the simple lie algebra an which admit a one dimensional weight space with respect to some cartan subalgebra h of a we first show that the problem is equivalent to determining all algebra homomorphisms from the centralizer of the cartan subalgebra h in the universal enveloping algebra of an to the base field we construct all such algebra homomorphisms and provide conditions under which two such algebra homomorphisms provide inequivalent irreducible representations of an

bosonization and integral representation of solutions of the knizhnik zamolodchikov bernard equations we construct an integral representation of solutions of the knizhnik zamolodchikov bernard equations using the wakimoto modules

irreducible representations of the lie algebra of the diffeomorphisms of ad dimensional torus in this paper we investigate the irreducibility of certain modules for the lie algebra of diffeomorphisms of torus t the lie algebra of diffeomorw 1 1 x phisms can be described as the derivations of a s c t t see 1 d w x w x rss we denote this lie algebra by der a larsson l1 constructed a functor from gl modules to der a modules in this paper we prove that d the image of a finite dimensional irreducible gl module is most often d irreducible the only exceptions are fundamental modules and the onedimensional modules in these cases we describe the sub modules and the quotients surprisingly the same class of modules image of finite dimen w x sional gl module are also constructed in e without any reference to d gl modules they are motivated by the vertex operator constructions in d w x em more details near the end of this introduction we will now describe our results in more detail let gl be the d lie algebras of d d matrices over complex numbers c let gl s sl d d c id where sl is the finite dimensional simple lie algebra of trace zero d matrices and id the identity matrix which is central it is well known that finite dimensional irreducible modules and dominant integral weights are in one one correspondence for a finite dimensional simple lie algebra so let v c be finite dimensional irreducible sl module corresponding to a d dominant integral weight c let id the central element act by a complex number b and denote the corresponding gl module by v c b d a d d larsson defined see 1 6 a functor f for a belonging to c rz from w x gl modules to der a modules in l1 these modules are weight modules d

representations of simple finite lie conformal superalgebras of type w and s we construct all finite irreducible modules over lie conformal superalgebras of type w and s

influence graphs and the generalized finite difference method this paper introduces directed graphs on which the evolution of a physical quantity depends only on local neighborhoods these graphs are then used to model transfer phenomena occurring under a convective mode or a diffusive mode the conditions under which the state associated to such graphs approaches the solution of a diffusion convection partial differential model are established an algorithm permitting to determine consistent neighborhoods is described and recognized as a generalization of the finite difference method examples of application are presented in order to illustrate the practical applicability of these concepts

categorification of the temperley lieb category tangles and cobordisms via projective functors to each generic tangle projection from the three dimensional real vector space onto the plane we associate a derived endofunctor on a graded parabolic version of the bernstein gel fand category mathcal o we show that this assignment is up to shifts invariant under tangle isotopies and reidemeister moves and defines therefore invariants of tangles the occurring functors are defined via so called projective functors the first part of the paper deals with the indecomposability of such functors and their connection with generalised temperley lieb algebras which are known to have a realisation via decorated tangles the second part of the paper describes a categorification of the temperley lieb category and proves the main conjectures of bfk moreover we describe a functor from the category of 2 cobordisms into a category of projective functors