ar X iv : 0 80 4 . 47 19 v 2 [ m at h . C O ] 1 9 M ay 2 00 8 COMBINATORIAL CONSTRUCTIONS OF WEIGHT BASES : THE GELFAND - TSETLIN BASIS

ar X iv : 1 60 5 . 07 58 0 v 1 [ m at h . R T ] 2 4 M ay 2 01 6 WEIGHT REPRESENTATIONS OF ADMISSIBLE AFFINE VERTEX ALGEBRAS

For an admissible affine vertex algebra Vk(g) of type A, we describe a new family of relaxed highest weight representations of Vk(g). They are simple quotients of representations of the affine Kac-Moody algebra ĝ induced from the following g-modules: 1) generic Gelfand-Tsetlin modules in the principal nilpotent orbit, in particular all such modules induced from sl2; 2) all Gelfand-Tsetlin modul...

ar X iv : 0 70 9 . 39 62 v 2 [ m at h . R T ] 2 6 M ar 2 00 8 COMBINATORIAL GELFAND MODELS

A combinatorial construction of a Gelfand model for the symmetric group and its Iwahori-Hecke algebra is presented.

ar X iv : 0 80 1 . 09 03 v 3 [ m at h . R A ] 6 J un 2 00 9 GELFAND - KIRILLOV CONJECTURE AND GELFAND - TSETLIN MODULES FOR FINITE W - ALGEBRAS

We address two problems regarding the structure and representation theory of finite W -algebras associated with the general linear Lie algebras. Finite W -algebras can be defined either via the Whittaker modules of Kostant or, equivalently, by the quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of the finite W a...

ar X iv : h ep - p h / 04 02 19 0 v 2 2 6 M ay 2 00 4 1 Pentaquarks in the 10 F - and 10 F - plets

ar X iv : 0 80 5 . 24 44 v 1 [ m at h . A G ] 1 6 M ay 2 00 8 Symmetry and holomorphy of the second member of the second Painlevé hierarchy

We study symmetry and holomorphy of the second member of the second Painlevé hierarchy P (2) II .