the theta characteristic of a branched covering abstract we give a group theoretic description of the parity of a pull back of a theta characteristic under a branched covering it involves lifting monodromy of the covering to the semidirect product of the symmetric and clifford groups known as the sergeev group as an application we enumerate torus coverings with respect to their ramification and parity and in particular show that the corresponding all degree generating functions are quasimodular forms

duality for ext groups and extensions of discrete series for graded hecke algebras in this paper we study extensions of graded affine hecke algebra modules in particular based on an explicit projective resolution on graded affine hecke algebra modules we prove a duality result for ext groups this duality result with an ind res resolution gives an algebraic proof of the fact that all higher ext groups between a tempered module and a discrete series vanish

on a theorem of benson and curtis iwahori conjectured 5 that the hecke algebra over q of a chevalley group g over a finite field f with respect to a bore1 subgroup is isomorphic to the group algebra over q of the weyl group the analogous statement with q replaced by its algebraic closure was proved by tits 3 ex 27 p 561 using a deformation argument in 11 benson and curtis proved using a case by case analysis that iwahori s conjecture is true over q whenever g is simple of type ze e with the help of springer they proved that when g is of type e or e there exists irreducible representations of the hecke algebra whose character involve 4 and hence iwahori s conjecture over q is false in general the main result of this paper is an explicit construction of an isomorphism of the hecke algebra over q q with the group algebra over q q of the weyl group the construction makes essential use of the polynomials p w of 8 at some point in the proof i have to appeal to the interpretation of p l in terms of multiplicities in verma modules 8 i 51 which has recently been established by brylinski and kashiwara 4 and independently by belinson and bernstein

a unification of knizhnik zamolodchikov and dunkl operators via affine hecke algebras some generalizations of the lusztig lascoux schutzenberger operators for affine hecke algebras are considered as corollaries we obtain lusztig s isomorphisms from affine hecke algebras to their degenerate versions a natural interpretation of the dunkl operators and a new class of differential difference operators generalizing dunkl s ones and the knizhnik zamolodchikov operators from the two dimensional conformal field theory

representations of rank two affine hecke algebras at roots of unity abstract in this paper we will fully describe the irreducible representations of the crystallographic rank two affine hecke algebras using algebraic and combinatorial methods for all possible values of q the focus is on the case when q is a root of unity of small order

localization for the evolution p laplacian equation with strongly nonlinear source term abstract in this paper we study the strict localization for the p laplacian equation with strongly nonlinear source term let u u x t be a solution of the cauchy problem u t div u p 2 u u q u x 0 u 0 x where x t r n 0 t n 1 and p 2 when q p 1 we prove that if the initial data u 0 x has a compact support then the solution u t has also compactly support moreover when 1 q p 1 we show that the solution of the cauchy problem blows up at any point of r n to arbitrary compactly supported initial data

regular articlethe structure of the young symmetrizers for spin representations of the symmetric group ii the first paper in this series established that the projective analogue of the young symmetrizer recently introduced by nazarov has a naturalpxq structure comparable with thepq form of the classical symmetrizer this second paper develops the theory on this decomposition further a more efficient construction of the projective symmetrizer is presented for certain classes of partitions this approach yields a compact expression for the intermediate factorx in the projective decomposition

on the category o for rational cherednik algebras we study the category o of representations of the rational cherednik algebra aw attached to a complex reflection group w w e construct an exact functor called knizhnik zamolodchikov functor o hw mod where hw is the finite iwahori hecke algebra associated to w we prove that the knizhnik zamolodchikov functor induces an equiv alence between o otor the quotient of o by the subcategory of aw modules supported on the discriminant and the category of finite dimensional hw modules the standard aw modules go under this equivalence to certain modules arising in kazhdan lusztig theory of cells provided w is a weyl group and the hecke algebra hw has equal parameters we prove that the category o is equivalent to the module category over a finite dimensional algebra a generalized q schur algebra associated to w

matrices characters and descents abstract a new family of asymmetric matrices of walsh hadamard type is introduced we study their properties and in particular compute their determinants and discuss their eigenvalues the invertibility of these matrices implies that certain character formulas are invertible yielding expressions for the cardinalities of sets of combinatorial objects with prescribed descent sets in terms of character values of the symmetric group

blocks of affine quantum schur algebras abstract the affine quantum schur algebra is a certain important infinite dimensional algebra whose representation theory is closely related to that of quantum affine gl n finite dimensional irreducible modules for the affine quantum schur algebra s n r v were classified in 15 where v c is not a root of unity we will classify blocks of the affine quantum schur algebra s n r v in this paper

relations between young s natural and the kazhdan lusztig representations of sn abstract our main result here is that under a suitable order of standard tableaux the classical representation of sn introduced by young in the collected papers of alfred young 1873 1940 univ of toronto press toronto qsa iv and usually referred as the natural representattion the the more recently discovered invent math 53 1979 165 184 kazhdan lusztig k l representation are related by an upper triangular integral matrix with unit diagonal elements we have been led to this discovery by a numerical exploration we noted it in each of the irreducible representations of sn up to n 6 the calculations in these cases were carried out by constructing the corresponding kazhdan lusztig graphs from tables m goresky tables of kazhdan lusztig polynomials unpublished of k l polynomials to extend the calculations to n 7 we have used graphs obtained by means of an algorithm given by lascoux and schutzenberger polynomes de kazhdan lusztig pour les grassmanniennes preprint remarkably the same property holds also for these graphs these findings appear to confirm the assertion made by these authors that their algorithm does indeed yield k l graphs for the case of hook shapes we have obtained an explicit construction of the transforming matrices a result which was also suggested by our numerical data for general shapes the transforming matrices are less explicit and our proof is based on certain properties of the kazhdan lusztig representations given in their article invent math 53 1979 165 184 and on a purely combinatorial construction of the natural representation

identification of simple representations for affine q schur algebras abstract we define an explicit action of the quantum loop algebra u q gl n on the tensor space and show that these actions are compatible with the natural embedding u q gl n u q gl n 1 as an application we identify simple representations of affine q schur algebras s n r c arising from simple polynomial representations of u q gl n frenkel and mukhin 2002 11 with those arising from simple modules of the affine hecke algebra h r c of type a rogawski 1985 26

partial regularity of strong local minimizers in the multi dimensional calculus of variations let n be a bounded domain and f a given strongly quasiconvex integrand of class c2 satisfying the growth condition f xi le c 1 xi p for some c 0 and 2 p consider the multiple integral i u int omega f nabla u where u w1 p n the main result of the paper is the proof that any strong local minimizer of i is of class c1 loc for any 0 1 on an open set of full n dimensional measure in the case of weak local minimizers we establish the same result under the extra assumption that the oscillations in the gradient of the minimizer are not too large without such an assumption weak local minimizers need not be partially regular as we show by a class of examples we also briefly discuss the question of existence of strong local minimizers for i and connections of our results to extensions of weierstrass sufficiency theorem to the multi dimensional setting

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

projective representations of symmetric groups via sergeev duality in this article we determine the irreducible projective representations of the symmetric group sd and the alternating group ad over an algebraically closed field of characteristic p 6 2 these matters are well understood in the case p 0 thanks to the fundamental work of schur 24 in 1911 as well as the much more recent work of nazarov 19 20 sergeev 25 26 and others so the focus here is primarily on the case of positive characteristic where surprisingly little is known as yet in particular we obtain a natural combinatorial labelling of the irreducibles in terms of a certain set rpp d of restricted p strict partitions of d such partitions arose recently in work of kashiwara miwa peterson and yung 11 and leclerc and thibon 14 on the q deformed fock space of the affine kac moody algebra of type a p 1 leclerc and thibon proposed that rpp d should label the irreducible projective representations in some natural way and we show here how this can be done note that for p 3 5 the labelling problem was solved in 1 3 while if p 2 all projective representations of sd and ad are linear so do not need to be considered further here to be more precise recall that is a partition of d if 1 2 is a non increasing sequence of non negative integers summing to d call p strict if in addition

a universal bound for radial solutions of the quasilinear parabolic equation with p laplace operator abstract in this paper we prove a universal bound for nonnegative radial solutions of the p laplace equation with nonlinear source u t div u p 2 u u q where p 2 and q p 1 this bound implies initial and final blowup rate estimates as well as a priori estimate or decay rate for global solutions our bound is proved as a consequence of liouville type theorems for entire solutions and doubling and rescaling arguments in this connection we use a known liouville type theorem for radial solutions along with a new liouville type theorem that is here established for nontrivial solutions in r

kazhdan lusztig immanants and products of matrix minors abstract using the kazhdan lusztig basis c w 1 w s n for the symmetric group algebra we obtain nonnegativity properties of certain polynomials in matrix minors in particular we show that the application of these polynomials to jacobi trudi matrices yields symmetric functions which are equal to nonnegative linear combinations of schur functions

some remarks concerning quasiconvexity and strong convergence we show that the weak convergence of a sequence of functions in a sobolev space plus the convergence of appropriately quasiconvex energies imply in fact strong convergence this assertion makes rigorous for example the heuristic principle that quasiconvexity damps out oscillations in the gradients of minimising sequences in the calculus of variations

on the cauchy problem for the evolution p laplacian equations with gradient term and source abstract in this paper the authors study the equation u t div d u p 2 d u u q 1 u d u l in r n with p 2 we first prove that for 1 l p 1 the solution exists at least for a short time then for p 2 l p 1 the existence and nonexistence of global in time solutions are studied in various situations

affine sergeev algebra and q analogues of the young symmetrizers for projective representations of the symmetric group we study a q deformation for the crossed product of the symmetric group s n with the clifford algebra on n anticommuting generators we obtain a q version of the projective analogue for the classical young symmetrizer introduced by the second author our main tool is an analogue of the hecke algebra of complex valued functions on the group mbox gl n over a p adic field relative to the iwahori subgroup

spin hecke algebras of finite and affine types we introduce the spin hecke algebra which is a q deformation of the spin symmetric group algebra and its affine generalization we establish an algebra isomorphism which relates our spin affine hecke algebras to the affine hecke clifford algebras of olshanski and jones nazarov relation between the spin affine hecke algebra and a nonstandard presentation of the usual affine hecke algebra is displayed and the notion of covering affine hecke algebra is introduced to provide a link between these algebras various algebraic structures for the spin affine hecke algebra are established

matrix coefficients and iwahori hecke algebra modules abstract we establish a connection between certain unique models or equivalently unique functionals for representations of p adic groups and linear characters of their corresponding hecke algebras this allows us to give a uniform evaluation of the image of spherical and iwahori fixed vectors in the unramified principal series for this class of models we provide an explicit alternator expression for the image of spherical vectors under these functionals in terms of the representation theory of the dual group

the brauer group of modified supergroup algebras abstract the computation of the brauer group bm of modified supergroup algebras over a field is performed yielding in particular the computation of the brauer group of all finite dimensional triangular hopf algebras when the base field is algebraically closed and of characteristic zero the used techniques are also applied for the computation of lazy cohomology of modified supergroup algebras we relate our construction with yinhuo zhang s exact sequence when the base ring is a field as an example we compute explicitly the brauer group and lazy cohomology for modified supergroup algebras with extensions of weyl groups of irreducible root systems as a group datum and their standard representation as a representation datum

periodic solutions of non newtonian polytropic filtration equations with nonlinear sources in this paper the authors first consider the dirichlet boundary value problem to the non newtonian polytropic filtration equation of the form u t div u m p 2 u m h x t u a in wxrwith strong nonlinear sources the existence of nontrivial periodic solutions is established based on topological degree theory the authors also studied the dirichlet boundary value problem to the equation in the form u t div u m 1u p 2 u m 1u b x t u f x t in wxrwith weak nonlinear sources the existence is treated with leray schauder fixed point theory

affine hecke algebras and generalized standard young tableaux abstract this paper introduces calibrated representations for affine hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations the primary technique is to provide indexing sets for controlling the weight space structure of finite dimensional modules for the affine hecke algebra using these indexing sets we show that 1 irreducible calibrated representations are indexed by skew local regions 2 the dimension of an irreducible calibrated representation is the number of chambers in the local region 3 each irreducible calibrated representation is constructed explicitly by formulas which describe the action of the generators of the affine hecke algebra on a specific basis in the representation space the indexing sets for weight spaces are generalizations of standard young tableaux and the construction of the irreducible calibrated affine hecke algebra modules is a generalization of a young s seminormal construction of the irreducible representations of the symmetric group in this sense young s construction has been generalized to arbitrary lie type

blow up results and global existence of positive solutions for the inhomogeneous evolution p laplacian equations abstract this paper deals with the cauchy problem of inhomogeneous evolution p laplacian equations t u div u p 2 u u q w x with nonnegative initial data where p 1 q max 1 p 1 and w x 0 is a nonnegative continuous functions in r n we prove that q c p 1 n n p is its critical exponent provided that 2 n n 1 p n i e if q q c then every positive solution blows up in finite time whereas for q q c the equation possesses a global positive solution for some w x and some initial data meanwhile we also prove that its positive solutions blow up in finite time provided that n p

spin nilhecke algebras of classical type abstract we formulate and study the spin nilhecke algebras nh n b and nh n d of type b d which differ from the usual nilhecke algebras by some odd signs the type b spin nilhecke algebra is a nil version of the spin type b hecke algebra introduced earlier by the second author and khongsap but not for the type d one we construct faithful polynomial representations pol n of the nilhecke algebras via odd demazure operators we formulate the spin schubert polynomials and use them to show that the spin nilhecke algebras are matrix algebras with entries in a subalgebra of pol n consisting of spin symmetric polynomials all these results have their counterparts for the usual nilhecke algebras over the rational field our work is a generalization of results of lauda and ellis khovanov lauda in usual spin type a

the projective representations of the hyperoctahedral group the hyperoctahedral group the weyl group of the root system bn has seven distinct nonsplit double covers for n 4 and hence seven families of projective representations we give constructions of all the irreducible representations of these seven double covers in terms of symmetric group representations and determine the associated character tables as a corollary we also obtain the irreducible projective representations and characters of the weyl group of the root system dn

on the cauchy problem for the evolution p laplacian equations with gradient term and source and measures as initial data abstract in this paper we study the cauchy problem for the evolution p laplacian equations with gradient term and source on the assumption that measures as initial conditions

lagrangian construction for representations of hecke algebras 1 let k be a non archimedean local field with the residue field consisting of q elements according to langlands philosophy irreducible complex representations of a reductive k group g should roughly speaking correspond to homomorphisms of the weil deligne group into the socalled l group let zc g be the iwahori subgroup the category of admissible gkmodules generated by z fixed vectors is known to be equivalent to the category of finite dimensional representations of the hecke algebra h z g z langlands philosophy suggests via that equivalence the following classification of irreducible hecke algebra modules stated in purely complex terms and not involving any local held

existence and nonexistence of global positive solutions for the evolution p laplacian equations in exterior domains abstract this paper deals with the existence and nonexistence of global positive solutions for two evolution p laplacian equations in exterior domains with inhomogeneous boundary conditions we demonstrate that q c n p 1 n p is its critical exponent provided 2 n n 1 p n furthermore we prove that if max 1 p 1 q q c then every positive solution of the equations blows up in finite time whereas for q q c the equations admit the global positive solutions for some boundary value f x and some initial data u 0 x we also demonstrate that every positive solution of the equations blows up in finite time provided n p

affine cellular algebras abstract graham and lehrer have defined cellular algebras and developed a theory that allows in particular to classify simple representations of finite dimensional cellular algebras many classes of finite dimensional algebras including various hecke algebras and diagram algebras have been shown to be cellular and the theory due to graham and lehrer successfully has been applied to these algebras we will extend the framework of cellular algebras to algebras that need not be finite dimensional over a field affine hecke algebras of type a and infinite dimensional diagram algebras like the affine temperley lieb algebras are shown to be examples of our definition the isomorphism classes of simple representations of affine cellular algebras are shown to be parameterised by the complement of finitely many subvarieties in a finite disjoint union of affine varieties in this way representation theory of non commutative algebras is linked with commutative algebra moreover conditions on the cell chain are identified that force the algebra to have finite global cohomological dimension and its derived category to admit a stratification these conditions are shown to be satisfied for the affine hecke algebra of type a if the quantum parameter is not a root of the poincare polynomial

quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity in this paper we prove the uniqueness of the solution to certain simple displacement boundary value problems in the nonlinear theory of homogeneous hyperelasticity for a body occupying a star shaped reference configuration rn whose boundary is subjected to an affine deformation i e there exists a constant n n matrix f and a constant n vector b such that x fx b for all x we consider all smooth equilibrium configurations satisfying this boundary condition clearly the homogeneous deformation x fx b for all x in bar omega is one such solution our aim is to prove under suitable hypotheses that it is the only such solution

yangian of the queer lie superalgebra consider the complex matrix lie superalgebra with the standard generators where define an involutory automorphism of by the twisted polynomial current lie superalgebra has a natural lie co superalgebra structure we quantise the universal enveloping algebra as a co poisson hopf superalgebra for the quantised algebra we give a description of the centre and construct the double in the sense of drinfeld we also construct a wide class of irreducible representations of the quantised algebra

crack growth in polyconvex materials we discuss a model for crack propagation in an elastic body where the crack path is described a priori in particular we develop in the framework of finite strain elasticity a rate independent model for crack evolution which is based on the griffith fracture criterion due to the nonuniqueness of minimizing deformations the energy release rate is no longer continuous with respect to time and the position of the crack tip thus the model is formulated in terms of the clarke differential of the energy generalizing the classical crack evolution models for elasticity with strictly convex energies we prove the existence of solutions for our model and also the existence of special solutions where only certain extremal points of the clarke differential are allowed

a categorification of twisted heisenberg algebras abstract we categorify a quantized twisted heisenberg algebra associated to a finite subgroup of sl 2 c

clifford algebra as quantum language we suggest clifford algebra as a useful simplifying language for present quantum dynamics clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups aggregates using such representations for their permutations obey clifford statistics the vectors supporting the clifford algebras of permutations and rotations are plexors and spinors respectively physical spinors may actually be plexors describing quantum ensembles not simple individuals we use clifford statistics to define quantum fields on a quantum space time and to formulate a quantum dynamics field space time unity that evades the compactification problem the quantum bits of history regarded as a quantum computation seem to obey a clifford statistics

the structure of the young symmetrizers for spin representations of the symmetric group i abstract this paper is the first in a series of three papers on the young symmetrizers for the spin representations of the symmetric group in this opening paper it is shown that the projective analogue of the young symmetrizer recently introduced by nazarov has a structure resembling thep q form exhibited by the classical symmetrizer in contrast to the classical case our decomposition of the projective symmetrizer requires an additional intermediate factorx this factor will be studied in greater detail in the later papers

the critical exponents for the quasi linear parabolic equations with inhomogeneous terms abstract this paper deals with the critical exponents for the quasi linear parabolic equations in r n and with an inhomogeneous source or in exterior domains and with inhomogeneous boundary conditions for n 3 2 n and p max 1 1 we obtain that p c n 1 n 2 is the critical exponent of these equations furthermore we prove that if max 1 1 p p c then every positive solution of these equations blows up in finite time whereas these equations admit the global positive solutions for some f x and some initial data u 0 x if p p c meantime we also demonstrate that every positive solution of these equations blows up in finite time provided n 1 2 1 and p max 1 1

non uniqueness of minimizers for strictly polyconvex functionals in this note we solve a problem posed by ball in philos trans r soc lond ser a 306 1496 557 611 1982 about the uniqueness of smooth equilibrium solutions to boundary value problems for strictly polyconvex functionals mathcal f u int omega f nabla u x rm d x quad rm and quad u vert partial omega u 0 where is homeomorphic to a ball

cocenters of hecke clifford and spin hecke algebras abstract we determine a basis of the cocenter i e the trace or zeroth hochschild homology of the degenerate affine hecke clifford and spin hecke algebras in classical types

the leading coefficient of certain kazhdan lusztig polynomials of the permutation group sn abstract in this paper we show that the leading coefficient y w of certain kazhdan lusztig polynomials p y w of the permutation group s n of 1 2 n are not greater than 1 more precisely we show that the leading coefficients y w are not greater than 1 whenever a y a w where a s n n is the function defined in g lusztig cells in affine weyl groups in algebraic groups and related topics in adv stud pure math vol 6 kinokunia north holland 1985 pp 255 287 see 1 5 for a simple interpretation of the function a

boolean elements in kazhdan lusztig theory abstract kazhdan lusztig polynomials have been proven to play an important role in different fields despite this there are still few explicit formulae for them here we give closed product formulae for the kazhdan lusztig polynomials indexed by boolean elements in a class of coxeter systems that we call linear boolean elements are elements smaller than a reflection that admits a reduced expression of the form s 1 s n 1 s n s n 1 s 1 s i s s i s j if i j then we provide several applications of this result concerning the combinatorial invariance of the kazhdan lusztig polynomials the classification of the pairs u v with u v the kazhdan lusztig elements and the intersection homology poincare polynomials of the schubert varieties

modules simples en caracteristique p de l algebre de hecke du pro p iwahori de gl3 f resume pour f un corps p adique et n n n 2 on ne connait pas de facon generale les representations lisses irreductibles modulo p de gl n f le foncteur des invariants par le pro p iwahori i 1 invite a les apprehender par l etude des modules simples a droite sur l algebre de hecke h f p gl n f i 1 dans le cas n 2 on connait les h f p gl n f i 1 modules simples ayant un caractere central parmi eux on distingue les modules que l on appelle supersinguliers ils ne correspondent pas via le foncteur des invariants par le pro p iwahori a des sous quotients d induites paraboliques de gl 2 f m f vigneras representations modulo p of the p adic group gl 2 f compos math 140 2004 333 358 nous considerons le cas n 3 il s agit de donner la classification des h f p gl 3 f i 1 modules simples ayant un caractere central et de decrire conjecturalement les modules supersinguliers l ensemble de ces modules supersinguliers est en bijection non unique avec l ensemble des f p representations irreductibles de dimension 3 du groupe de weil de f

an optimal liouville type theorem of the quasilinear parabolic equation with a p laplace operator abstract in this paper we consider nonnegative solutions of the quasilinear parabolic equation with p laplace operator u t div u p 2 u u q 1 u where p 2 and q p 1 our main result is that there is no nontrivial positive bounded radial entire solution the proof is based on intersection comparison arguments which can be viewed as a sophisticated form of the maximum principle and has been used to deal with the semilinear heat equation by polacik and quittner peter polacik pavol quittner a liouville type theorem and the decay of radial solutions of a semilinear heat equation nonlinear analysis tma 64 2006 1679 1689 and the porous medium equation by souplet ph souplet an optimal liouville type theorem for radial entire solutions of the porous medium equation with source j differential equations 246 2009 3980 4005

the regularity of critical points of polyconvex functionals in this paper we are concerned with the question of regularity of critical points for functionals of the type eq1 we construct a smooth strongly polyconvex eq2 and lipschitzian weak solutions eq3 to the corresponding euler lagrange system which are nowhere c1 moreover we show that f can be chosen in such a way that these irregular weak solutions are weak local minimisers

degenerate affine hecke algebras and centralizer construction for the symmetric groups in our recent papers the centralizer construction was applied to the series of classical lie algebras to produce the quantum algebras called twisted yangians here we extend this construction to the series of the symmetric groups s n we study the stable properties of the centralizers of s n m in the group algebra c s n as n with m fixed we construct a limit centralizer algebra a and describe its algebraic structure the algebra a turns out to be closely related with the degenerate affine hecke algebras we also show that the so called tame representations of s yield a class of natural a modules

type a blocks of super category o we show that every block of category oo for the general linear lie superalgebra glm n k glm n k is equivalent to some corresponding block of category oo for the queer lie superalgebra qm n k qm n k this implies the truth of the kazhdan lusztig conjecture for the so called type a blocks of category oo for the queer lie superalgebra as formulated by cheng kwon and wang

on the classification of finite dimensional irreducible modules for affine bmw algebras in this paper we classify the finite dimensional irreducible modules for affine bmw algebra over an algebraically closed field with arbitrary characteristic

local minimizers and quasiconvexity the impact of topology the aim of this paper is to discuss the question of existence and multiplicity of strong local minimizers for a relatively large class of functionals open image in new window open image in new window from a purely topological point of view the basic assumptions on open image in new window are sequential lower semicontinuity with respect to w1 p weak convergence and w1 p weak coercivity and the target is a multiplicity bound on the number of such minimizers in terms of convenient topological invariants of the manifolds open image in new window and open image in new window

extinction and non extinction for a p laplacian equation with nonlinear source abstract in this paper we deal with the extinction of solutions of the initial boundary value problem of the p laplacian equation u t div u p 2 u u q in a bounded domain of r n with n 2 for 1 p 2 we show that q p 1 is the critical exponent of extinction for the weak solution furthermore for 1 p 2 and q p 1 we prove that the extinction and non extinction of the solution depends strongly on the first eigenvalue of the problem div p 2 p 2 in 0

local and global existence for quasilinear parabolic systems with a strongly nonlinear source abstract we study the cauchy problem for quasilinear parabolic systems with a strongly nonlinear source on the assumptions that the initial values are taken in the sense of l l o c 1 r n we obtain the local existence global existence and nonexistence of solutions particularly in the case of global solvability some exact estimates of a solution are obtained

kazhdan lusztig representations and whittaker space of some genuine representations we prove a formula for the dimension of whittaker functionals of irreducible constituents of a regular unramified genuine principal series for covering groups the formula explicitly relates such dimension to the kazhdan lusztig representations associated with certain right cells of the weyl group we also state a refined version of the formula which is proved under some natural assumption the refined formula is also verified unconditionally in several important cases

convexity conditions for strain dependent energy functions for membranes the forms that the convexity polyconvexity and rank one convexity inequalities take when the strain energy is required to be a function of the strain g are studied it is shown in particular that w g must be an increasing function of g in the sense that w g w g if g g is non negative definite relatively simple sufficient conditions in terms of g alone are given necessary and sufficient conditions in terms of g alone are found to be rather complex

rational and polynomial representations of yangians abstract we define natural classes of rational and polynomial representations of the yangian of the general linear lie algebra we also present the classification and explicit realizations of all irreducible rational representations of the yangian

drinfeld functor and finite dimensional representations of yangian we extend the results of drinfeld on the drinfeld functor to the case l n we present the character of finite dimensional representations of the yangian y mathfrak s mathfrak l n in terms of the kazhdan lusztig polynomials as a consequence

twisted vertex representations and spin characters we establish a new group theoretic realization of the basic representations of the twisted affine and twisted toroidal algebras in the same spirit of our new approach to the mckay correspondence our vertex operator construction provides a unified description to the character tables for the spin cover of the wreath product of the twisted hyperoctahedral groups and an arbitrary finite group

equivariant k theory generalized symmetric products and twisted heisenberg algebra for a space x acted on by a finite group the product space xn affords a natural action of the wreath product n n sn the direct sum of equivariant k groups were shown earlier by the author to carry several interesting algebraic structures in this paper we study the k groups of n equivariant clifford supermodules on xn we show that is a hopf algebra and it is isomorphic to the fock space of a twisted heisenberg algebra twisted vertex operators make a natural appearance the algebraic structures on x when is trivial and x is a point specialize to those on a ring of symmetric functions with the schur q functions as a linear basis as a by product we present a novel construction of k theory operations using the spin representations of the hyperoctahedral groups

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

shifted tableaux and the projective representations of symmetric groups les groupes de representation de s n classes de conjugaison algebres de clifford et la representation spin de base produits induits pour des representations spin une application caracteristique pour des caracteres de spin tableaux decales et q fonctions de schur les caracteres de spin irreductibles de s n et a n une analogue decalee de la regle lr produits tensoriels interieurs

hecke clifford algebras and spin hecke algebras iii the trigonometric type abstract the notions of trigonometric spin double affine hecke algebras tsdaha and trigonometric double affine hecke clifford algebras tdahca associated to classical weyl groups are introduced the pbw basis property is established an algebra isomorphism relating tdahca to tsdaha is obtained

periodic solutions of evolutionp laplacian equations with nonlinear sources abstract in this paper we are concerned with the time periodic solutions to the evolution p laplacian equations of the form formula and formula with the dirichlet boundary value condition where p 2 0 is a bounded convex domain in r n with smooth boundary m x t is continuous on r periodic in t with period and positive in r the existence of nontrivial nonnegative periodic solutions is established provided that n 1 and p 1 p 1 p n