raising and lowering operators for uq gl n a set of raising and lowering operators are constructed for uq gl n being hermitian conjugates of one another they are easily normalized and allow us to express arbitrary gelfand tzetlin basis states as a product of lowering operators acting on the maximal weight state

a non local elliptic hyperbolic system related to the short pulse equation abstract in this paper we prove the well posedness of a non local elliptic hyperbolic system related to the short pulse equation it is a model which describes the evolution of the electrical field of linearly polarized continuum spectrum pulses in optical waveguides including fused silica telecommunication type or photonic crystal fibers as well as hollow capillaries filled with transparent gases

symmetries of clebsch gordan coefficients of the quantum group uq n permutation symmetries for clebsch gordan coefficients of the quantum group uq n and for uq n 1 reduced clebsch gordan coefficients of uq n are derived in particular the formula relating clebsch gordan coefficients for the tensor product tm1 tm2 with clebsch gordan coefficients for the tensor product with permuted representations tm1 and tm is obtained where tm is one of the irreducible representations in the decomposition of tm1 tm2 contrary to the classical case coefficients connecting these clebsch gordan coefficients depend on gel fand tsetlin patterns of one of irreducible representations this dependence is explicitly determined

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

matrix elements and wigner coefficients for uq gl n in this series of papers the fundamental wigner coefficients and the matrix elements of the generators for the quantum group uq gl n are derived the uq gl n uq gl n 1 reduced wigner coefficients and reduced matrix elements are determined algebraically as eigenvalues of certain uq gl n 1 invariants in the quantum group uq gl n the matrix elements of the elementary quantum group generators in the gel fand tsetlin basis are derived below while all fundamental wigner coefficients are derived in the second paper of the series

tensor operators and projection techniques in infinite dimensional representations of semi simple lie algebras polynomial identities satisfied by the infinitesimal generators of a semi simple lie group are employed to construct projection operators which project a tensor product representation v lambda x v v lambda finite dimensional and irreducible v an infinite dimensional representation admitting an infinitesimal character onto a primary subrepresentation such projection operators project out the generalised shift components of a tensor operator acting on an infinite dimensional representation v in direct analogy with the finite dimensional analysis of bracken and green 1971 applications of these methods to evaluating the matrix elements of the generators of the locally compact groups u p q and o p q in unitary discrete irreducible representations are discussed

the second homology group of the mapping class group of an orientable surface in i 7 mumford shows that the picard group p ic is isomorphic to h2 f 2 and conjectures the latter is rank one g 3 we prove this below for g 5 another interpretation of this theorem may be obtained by identifying h2 f as bordism classes of fiber bundles f w4 t where t is a closed oriented surface sect 0 when f is closed every such bundle is bordant to f w t a bundle admitting a section s t w the theorem then says that

counting on ctl on the expressive power of monadic path logic monadic second order logic msol provides a general framework for expressing properties of reactive systems as modelled by trees monadic path logic mpl is obtained by restricting second order quantification to paths reflecting computation sequences in this paper we show that the expressive power of mpl over trees coincides with the usual branching time logic ctl embellished with a simple form of counting as a corollary we derive an earlier result that ctl coincides with the bisimulation invariant properties of mpl in order to prove the main result we first prove a new composition theorem for trees

string theory and algebraic geometry of moduli spaces it is shown how the algebraic geometry of the moduli space of riemann surfaces entirely determines the partition function of polyakov s string theory this is done by using elements of arakelov s intersection theory applied to determinants of families of differential operators parametrized by moduli space as a result we write the partition function in terms of exponentials of arakelov s green functions and faltings invariant on riemann surfaces generalizing to arithmetic surfaces i e surfaces which are associated to an algebraic number fieldk we establish a connection between string theory and the infinite primes ofk as a result we conjecture that the usual partition function is a special case of a new partition function on the moduli space defined overk

biorthogonal coupling coefficients of uq n the coupling wigner clebsch gordan coefficients and their isofactors for the unitary quantum algebras uq n with the repeating irreducible representations in the coproduct decomposition are considered generalizing the u n case the biorthogonal systems of the uq n isofactors with the dual multiplicity labels are constructed by means of the recoupling technique in terms of the isofactors with simpler multiplicity structure a first construction correlated with the inverted littlewood richardson rules gives the bilinear combinations of isofactors after applying the proportionality of the q recoupling racah coefficients to the boundary q isofactors an alternative recursive construction gives the nonorthogonal q isofactors satisfying the most elementary boundary conditions and proportional to the uq n 1 recoupling coefficients for some less restricted values of parameters some multiplicity free and more general uq n recoupling coefficients are found the blocks bilinear combinations of which equal to the resubducing coefficients of the complementary chains of q algebras are proposed to use for the orthonormalization of some uq n biorthogonal isofactors including the general uq 3 case

wigner coefficients for a semisimple lie group and the matrix elements of the o n generators a purely algebraic infinitesimal method for obtaining multiplicity free wigner coefficients is presented the method is applied to obtain analytic expressions for the complete matrix elements of all o n generators moreover the structure of these matrix elements in terms of reduced matrix elements wigner coefficients and reduced wigner coefficients is made explicit by comparison with the wigner eckart theorem explicit analytic expressions are obtained for the fundamental wigner coefficients of o n finally the results are presented in a form which is directly analogous with the corresponding results for u n

multiplicity free uq n coupling coefficients the coupling wigner clebsch gordan coefficients of the unitary quantum algebras uq n are considered the tensorial properties of the generator powers and their ordered products used in the explicit projectors and weight lowering procedures are established different expressions for the multiplicity free isofactors of uq n coupling coefficients those coupling an arbitrary and symmetric representations are derived explicit expression of the arbitrary isofactors in terms of their boundary values are proposed proportionality of the semistretched isofactors to the stretched q recoupling coefficients of uq n 1 q analogues of 9j symbols is demonstrated the stretched isofactors of uq 3 are expressed in terms of clebsch gordan coefficients of uq 2

existence uniqueness and regularity of multi dimensional nonlocal balance laws with damping abstract in this article we generalize some existence and uniqueness results in 22 for scalar nonlocal balance laws to multi dimensional nonlocal balance laws also in the multi dimensional case it is possible to get rid of the entropy condition which is usually postulated to guarantee a unique weak solution of local balance laws but which we prove to be redundant in the nonlocal case we start with a well known existence theorem for linear balance laws and the explicit formula for a solution to obtain a fixed point problem in the nonlocal term using banach s fixed point theorem we prove existence and uniqueness of a fixed point this existence and uniqueness result is used for constructing and proving a unique solution of the multi dimensional nonlocal balance law on a sufficiently small time horizon while in many publications the nonlocal term will be considered over the entire space domain we present an existence and uniqueness result which allows rather general integration areae for the nonlocal term eventually we obtain a unique weak solution on every finite time horizon existence and uniqueness are complemented by stability results and an exhaustive study on more regular weak solutions in case the data is more regular

the boson realizations of the quantum group uq sl 2 the method of construction of boson realizations of semisimple lie algebras formulated in a previous paper is applied to the case of the quantum group uq sl 2 the realizations are expressed in terms of the usual weyl algebra

matrix elements for type 1 unitary irreducible representations of the lie superalgebra gl m n using our recent results on eigenvalues of invariants associated to the lie superalgebra gl m n we use characteristic identities to derive explicit matrix element formulae for all gl m n generators particularly non elementary generators on finite dimensional type 1 unitary irreducible representations we compare our results with existing works that deal with only subsets of the class of type 1 unitary representations all of which only present explicit matrix elements for elementary generators our work therefore provides an important extension to existing methods and thus highlights the strength of our techniques which exploit the characteristic identities

a quantum group structure in integrable conformal field theories we discuss a quantization prescription of the conformal algebras of a class ofd 2 conformal field theories which are integrable we first give a geometrical construction of certain extensions of the classical virasoro algebra known as classicalw algebras in which these algebras arise as the lie algebra of the second hamiltonian structure of a generalized korteweg de vries hierarchy this fact implies that thew algebras obtained as a reduction with respect to the nilpotent subalgebras of the kac moody algebra describe the integrability of a toda field theory subsequently we determine the coadjoint operators of thew algebras and relate these to classical yang baxter matrices the quantization of these algebras can be carried out using the concept of a so called quantum group we derive the condition under which the representations of these quantum groups admit a hilbert space completion by exploring the relation with the braid group then we consider a modification of the miura transformation which we use to define a quantumw algebra this leads to an alternative interpretation of the coset construction for kac moody algebras in terms of nonlinear integrable hierarchies subsequently we use the connection between the induced braid group representations and the representations of the mapping class group of riemann surfaces to identify an action of thew algebras on the moduli space of stable curves and we give the invariants of this action this provides a generalization of the situation for the virasoro algebra where such as invariant is given by the so called mumford form which describes the partition function of the bosonic string

arity hierarchy for temporal logics a major result concerning temporal logics is kamp s theorem which states that the pair of modalities until and since is expressively complete for the first order fragment of the monadic logic over the linear time canonical model of naturals the paper concerns the expressive power of temporal logics over trees the main result states that in contrast to kamp s theorem for every n there is a modality of arity n definable by a monadic logic formula which is not equivalent over trees to any temporal logic formula which uses modalities of arity less than n its proof takes advantage of an instance of shelah s composition theorem this result has interesting corollaries for instance reproving that ctl and ectl have no finite basis

compatible poisson structures and the virasoro algebra this paper is dedicated to henry mckean whose master craftsmanship enriched such diverse areas of mathematics and provided his disciples with a lofty measure by which to gauge their efforts and so redouble them

multiplicity free wigner coefficients for semisimple lie groups i the u n pattern calculus this is the first paper in a series of two dedicated to a new algebraic determination of the multiplicity free reduced wigner coefficients for the lie groups u n and o n the approach employed enables a direct nonrecursive derivation of reduced wigner coefficients the absolute value squared of the reduced wigner coefficients is expressed as a rational polynomial function numerator polynomial divided by denominator polynomial whose weyl group symmetries are seen to fall out naturally in our approach from the transformation properties of polynomial functions determined by casimir invariants a unified treatment of the composition laws of reduced wigner coefficients and the evaluation of their associated denominator polynomials is presented which applies to both u n and o n an explicit formula for the numerator polynomials of u n is also derived the numerator polynomials for the orthogonal groups will be given in the second paper of the series

some symmetries of quantum dimensions several useful properties of the quantum dimensions of representations of uq sl n for q a root of unity are established the results can be used to calculate truncated kronecker products of these representations and hence to investigate the isomorphism between these truncated tensor products and the fusion rules of the wzw theories associated with uq sl n

generalized gel fand invariants and characteristic identities for quantum groups the generalized gel fand invariants for an arbitrary quantum group are explicitly constructed and their eigenvalues in any irreducible representation are computed these invariants enable one to develop characteristic identities for the quantum group and as a natural application these identities are used to construct projection operators for tensor products of representations to illustrate the general theory the quantum group uq gl m is studied in detail

well posedness of a conservation law with non local flux arising in traffic flow modeling we prove the well posedness of entropy weak solutions of a scalar conservation law with non local flux arising in traffic flow modeling the result is obtained providing accurate mathbf l infty l bv and mathbf l 1 l1 estimates for the sequence of approximate solutions constructed by an adapted lax friedrichs scheme

moduli spaces of curves and representation theory we establish a canonical isomorphism between the second cohomology of the lie algebra of regular differential operators on x of degree 1 and the second singular cohomology of the moduli space hat f g 1 of quintuples c p z l wherec is a smooth genusg riemann surface p a point onc z a local parameter atp l a degreeg 1 line bundle onc and a class of local trivializations ofl atp which differ by a non zero factor the construction uses an interplay between various infinite dimensional manifolds based on the topological spaceh of germs of holomorphic functions in a neighborhood of 0 in x and related topological spaces the basic tool is a canonical map from hat f g 1 to the infinite dimensional grassmannian of subspaces ofh which is the orbit of the subspaceh of holomorphic functions on x vanishing at under the group auth as an application we give a lie algebraic proof of the mumford formula n 6n2 6n 1 1 where n is the determinant line bundle of the vector bundle on the moduli space of curves of genusg whose fiber overc is the space of differentials of degreen onc

n 2 super w algebras and generalized n 2 super kdv heirarchies based on lie superalgebras the authors propose a hierarchy of super lax equations based on an affine lie superalgebra a n n 1 as the generalized n 2 super kdv hierarchy and show that the associated super gel fand dikii bracket defines an n 2 super w algebra for a 2 2 1 they obtain the n 2 super boussiensque equation and the n 2 super w2 algebra containing additional currents of spins 2 5 2 3

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

nonlocal systems of balance laws in several space dimensions with applications to laser technology for a class of systems of nonlinear and nonlocal balance laws in several space dimensions we prove the local in time existence of solutions and their continuous dependence on the initial datum the choice of this class is motivated by a new model devoted to the description of a metal plate being cut by a laser beam using realistic parameters solutions to this model obtained through numerical integrations meet qualitative properties of real cuts moreover the class of equations considered comprises a model describing the dynamics of solid particles along a conveyor belt

the complexity of propositional linear temporal logics in simple cases it is well known that model checking and satisfiability for pltl are pspace complete by contrast very little is known about whether there exist some interesting fragments of pltl with a lower worst case complexity such results would help understand why pltl model checkers are successfully used in practice in this article we investigate this issue and consider model checking and satisfiability for all fragments of pltl obtainable by restricting 1 the temporal connectives allowed 2 the number of atomic propositions and 3 the temporal height 2002 elsevier science usa

hidden quantum group symmetry and integrable perturbations of conformal field theories the hidden quantum group symmetry in the quantum sine gordon model is found this symmetry provides the possibility to restrict the operator algebra of the model to subalgebras it is shown that these subalgebras are massive deformations of minimal conformal field theories

efficient timed model checking for discrete time systems we consider model checking of timed temporal formulae in durational transition graphs dtgs i e kripke structures where transitions have integer durations two semantics for dtgs are presented and motivated we consider timed versions ofctl where subscripts put quantitative constraints on the time it takes before a property is satisfied we exhibit an important gap between logics where subscripts of the form c exact duration are allowed and simpler logics that only allow subscripts of the form c or c bounded duration without exact durations model checking can be done in polynomial time but with exact durations it becomes 2p complete or pspace complete depending on the considered semantics

coadjoint orbits of the virasoro group the coadjoint orbits of the virasoro group which have been investigated by lazutkin and pankratova and by segal should according to the kirillov kostant theory be related to the unitary representations of the virasoro group in this paper the classification of orbits is reconsidered with an explicit description of the possible centralizers of coadjoint orbits the possible orbits are diff s1 itself diff s1 s1 and diff s1 sl n 2 r withsl n 2 r a certain discrete series of embeddings ofsl 2 r in diff s1 and diffs1 t wheret may be any of certain rather special one parameter subgroups of diffs1 an attempt is made to clarify the relation between orbits and representations it appears that quantization of diffs1 s1 is related to unitary representations with nondegenerate kac determinant unitary verma modules while quantization of diffs1 sl n 2 r is seemingly related to unitary representations with null vectors in leveln a better understanding of how to quantize the relevant orbits might lead to a better geometrical understanding of virasoro representation theory in the process of investigating virasoro coadjoint orbits we observe the existence of left invariant symplectic structures on the virasoro group manifold as is described in an appendix these give rise to lie bialgebra structures with the virasoro algebra as the underlying lie algebra

the initial boundary value problem for general non local scalar conservation laws in one space dimension we prove global well posedness results for weak entropy solutions of bounded variation bv of scalar conservation laws with non local flux on bounded domains under suitable regularity assumptions on the flux function in particular existence is obtained by proving the convergence of an adapted lax friedrichs algorithm lipschitz continuos dependence from initial and boundary data is derived applying kru hkov s doubling of variable technique

the symplectic nature of fundamental groups of surfaces soit 7b g la categorie des groupes de lie g avec une forme bilineaire symetrique non singuliere b sur l algebre de lie soit le groupe fondamental d une surface orientee close de genre 1 et soit 7b s la categorie des out espaces symplectiques alors la correspondance g b hom g g b definit un foncteur 7b g 7b s ou b est la structure symplectique sur hom g g definie par b

the mumford form and the polyakov measure in string theory an explicit formula is derived for the mumford form on the moduli space of algebraic curves according to the belavin knizhnik theorem this gives a formula for the polyakov bosonic string measure

on approximation of local conservation laws by nonlocal conservation laws abstract we show that for monotone initial datum the solution of nonlocal conservation laws converges to the entropy solution of the corresponding local conservation laws when the nonlocal reach tends to zero this particularly covers the principle cases of conservation laws shocks and rarefactions the considered problem is addressed by studying the entropy of the nonlocal conservation laws in the limit and by exploiting the semi explicit solution formula developed in 30

universal r matrices and invariants of quantum supergroups a general method is developed for constructing invariants of quantum supergroups using universal r matrices applied to uq gl 2 1 this method yields the invariants of this quantum supergroup in explicit form the eigenvalues of these invariants in arbitrary irreducible highest weight representations are computed

reduced wigner coefficients for uq gl n this is the second paper in a series concerned with the racah wigner calculus for the quantum group uq gl n in this approach all reduced wigner coefficients are determined algebraically by the eigenvalues of certain generalized casimir invariants here the method is applied to evaluate all fundamental wigner coefficients and reduced wigner coefficients for uq gl n

nonlocal systems of conservation laws in several space dimensions we present a lax friedrichs type algorithm to numerically integrate a class of nonlocal and nonlinear systems of conservation laws in several space dimensions the convergence of the approximate solutions is proved also providing the existence of a solution in a slightly more general setting than in other results in the current literature an application to a crowd dynamics model is considered

classical w algebras we reconsider the relation between classicalw algebras and deformations of differential operators emphasizing the consistency with diffeomorphisms generators of thew algebra that arek differentials are constructed by a systematic procedure the method extends following drinfeld and sokolov tow algebras based on arbitrary simple lie algebras

an infinite hierarchy of temporal logics over branching time many temporal logics have been suggested as branching time specification formalisms during the past 20 years these logics were compared against each other for their expressive power model checking complexity and succinctness yet unlike the case for linear time logics no canonical temporal logic of branching time was agreed upon we offer an explanation for the multiplicity of temporal logics over branching time and provide an objective quantified yardstick to measure these logics we define an infinite hierarchy btlk of temporal logics and prove its strictness we examine the expressive power of commonly used branching time temporal logics we show that ctl has no finite base and that almost all of its many sublogics suggested in the literature are inside the second level of our hierarchy we introduce new ehrenfeucht fraisse games on trees and use them as our main tool to prove inexpressibility 2001 elsevier science

multiplicity free wigner coefficients for semisimple lie groups ii a pattern calculus for o n in this paper a direct algebraic derivation of a large class of multiplicity free reduced wigner coefficients is presented for the orthogonal groups in particular all elementary reduced wigner coefficients including those for the fundamental spinor and tensor representations are obtained the results are presented in a form directly analogous to the corresponding results obtained for the unitary groups

invariants and matrix elements of the quantum group u_q gl n mathbb c revisited in a previous paper the generator matrix elements and dual vector reduced wigner coefficients rwcs were evaluated via the polynomial identities satisfied by a certain matrix constructed from the r matrix r and its twisted counterpart r t t circle r here we provide an alternative evaluation utilising the r matrix r over tilde r t 1 this provides a new direct derivation of the vector rwcs obtained indirectly in earlier work via a symmetry relation this approach has the advantage that it generalises to the lie superalgebra case which will be investigated elsewhere

finite volume schemes for nonhomogeneous scalar conservation laws error estimate in this paper we study finite volume schemes for the nonhomogeneous scalar conservation law u t rm div f x t u q x t u with initial condition u x 0 u0 x the source term may be either stiff or nonstiff in both cases we prove error estimates between the approximate solution given by a finite volume scheme the scheme is totally explicit in the nonstiff case semi implicit in the stiff case and the entropy solution the order of these estimates is h frac 1 4 in space time l 1 norm h denotes the size of the mesh furthermore the error estimate does not depend on the stiffness of the source term in the stiff case

the yang baxter equation and invariants of links on considere le fait que l on peut construire des invariants d isotopie p et f pour des liens en utilisant certaines solutions des equations de yang baxter

the complexity of propositional linear temporal logics the complexity of satisfiability and determination of truth in a particular finite structure are considered for different propositional linear temporal logics it is shown that these problems are np complete for the logic with f and are pspace complete for the logics with f x with u with u s x operators and for the extended logic with regular operators given by wolper

solutions of the graded classical yang baxter equation and integrable models linear superalgebraic equations giving rise to solutions of the graded classical yang baxter equation are developed and solved explicitly the connection of these equations with the theory of lie bi superalgebras is pointed out and the possibility of using the solutions of the graded classical yang baxter equation to construct integrable supersymmetric models is discussed

a matrix integral solution to two dimensional w p gravity thep th gel fand dickey equation and the string equation l p 1 have a common solution expressible in terms of an integral overn n hermitean matrices for largen the integrand being a perturbation of a gaussian generalizing kontsevich s integral beyond the kdv case it is equivalent to showing that is a vacuum vector for aw generated from the coefficients of the vertex operator this connection is established via a quadratic identity involving the wave function and the vertex operator which is a disguised differential version of the fay identity the latter is also the key to the spectral theory for the two compatible symplectic structures of kdv in terms of the stress energy tensor associated with the virasoro algebra given a differential operator l d p q 2 t d p 2 cdots q p t with d frac partial dx t t 1 t 2 t 3 x equiv t 1 consider the deformation equations1 0 1 begin gathered frac partial l partial t n l n p l n 1 2 n 0 mod p hfill p reduced kp equation hfill end gathered ofl for which there exists a differential operatorp possibly of infinite order such that 0 2 l p 1 string equation in this note we give a complete solution to this problem in section 1 we give a brief survey of useful facts about thei function t the wave function t z solution of t n l n p x andl 1 p z and the corresponding infinitedimensional planev 0 of formal power series inz for largez v 0 span psi t z for all t in mathbb c infty in sato s grassmannian the three theorems below form the core of the paper their proof will be given in subseuqent sections each of which lives on its own right

enveloping algebra annihilators and projection techniques for finite dimensional cyclic modules of a semisimple lie algebra some results on the structure of finite dimensional cyclic modules for a semisimple lie algebra are presented cyclic modules arise naturally in constructing symmetry adapted states of a system using projection projecting out states with definite symmetry from an arbitrary state is related to the properties of the cyclic module generated by an important example of a cyclic module is the tensor product of two irreducible modules v v which is cyclically generated by the vector v v where v resp v is the minimal resp maximal weight vector of v resp v for this particular case we determine the explicit form of the annihilator in the universal enveloping algebra of the cyclic vector v v it is hoped that this result may add new insight into the clebsch gordan multiplicity problem as an application of this result projection operators are constructed which project from an arbitrary vector of weight a maximal weight vector of weight

classification of unitary and grade star irreps for uq osp 2 2n all the unitary and grade star irreps of the quantum supergroup uq osp 2 2n are classified in terms of their highest weight labels

btl 2 and the expressive power of ectl we show that ectl the classical extension of ctl with fairness properties is expressively equivalent to btl2 a natural fragment of the monadic logic of order btl2 is the branching time logic with arbitrary quantification over paths and where path formulac are restricted to quantifier depth 2 first order formulae in the monadic logic of order this result linking ectl to a natural fragment of the monadic logic of order provides a characterization that other branching time logics e g ctl lack we then go on to show that ectl and btl2 are not finitely based i e they cannot be defined by a finite set of temporal modalities and that their model checking problems are of the same complexity