Standard multipartitions and a combinatorial affine Schur-Weyl duality

：万金奎（北京理工大学）
：2022-12-08 15:00
：腾讯会议ID：446 -977-521（无密码）

报告人：万金奎（北京理工大学）

时  间：12月8日下午15:00-16:30

地  点：腾讯会议ID：446 -977-521（无密码）

内容摘要:

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.

个人简介：

万金奎，北京理工大学数学与统计学院，教授，博导，主要从事李代数、量子群、赫克代数及相关代数的表示理论以及相应的代数组合理论的研究。2021年获国家自然科学基金优秀青年科学基金。研究成果发表在Proc. Lond. Math. Soc、Adv. Math. 、Trans. Amer. Math. Soc、Int Math Res Notices等国际数学杂志。

 

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