Speaker：Jinkui Wang（Beijing Institute of Technology）

Time：2022-12-08, 15:00

Location：Tencent Meeting ID：446 -977-521（No Password）

Abstract:

We introduce the notion of standard (Kleshchev) multipartitions and establish a one-to-one correspondence between standard multipartitions and irreducible representations with integral weights for the affine Hecke algebra of type A with a parameter q which is not a root of unity. We then extend the correspondence to all Kleshchev multipartitions for Ariki-Koike algebras of integral type. By the affine Schur–Weyl duality, we further extend this to a correspondence between standard multipartitions and Drinfeld multipolynomials of integral type whose associated irreducible polynomial representations completely determine all irreducible polynomial representations for the quantum loop algebra associated to gl_n. We show, in particular, the notion of standard multipartitions gives rise to a combinatorial description of the affine Schur–Weyl duality in terms of a column-reading vs. row-reading of residues of a multipartition. This is based on a joint work with Jie Du.