报告题目 (Title)：双i量子群U^j（n）和U^i（n）
The twin i-quantum groups U^j(n) and U^i(n)
报告人 (Speaker)：Jie Du教授（澳大利亚新南威尔士大学）
报告时间 (Time)：2025年3月25日 (周二) 16:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：张红莲教授
主办部门：理学院数学系
报告摘要： When I. Schur used representations of the symmetric groups S_r to determine polynomial representations of the complex general linear group GL_n(C), certain finite-dimensional algebras, known as Schur algebras, played a bridging role between the two. The well-known Schur duality summarizes the relation between the representations of GL_n(C) and S_r. Over almost a hundred years, this duality has profoundly influenced representation theory and has evolved in various forms such as the Schur-Weyl duality, Schur-Weyl-Brauer duality, Schur-Weyl-Sergeev duality, and so on. In this talk, I will discuss a latest development, which I call the Schur-Weyl-Hecke duality, by Huanchen Bao and Weiqiang Wang. Based on joint work with Yadi Wu, I will focus on the investigation of the i-quantum groups U^j(n) and U^i(n) and their associated q-Schur algebras S^j(n, r) and S^i(n, r) of types B and C, respectively. This includes short (element) multiplication formulas, long (element) multiplication formulas, and triangular relations in S^j(n, r) and S^i(n, r). We will also give realisations of Beilinson–Lusztig–MacPherson type for both U^j(n) and U^i(n) and discuss their Lusztig forms. This allows us to link representations of U^j(n) and U^i(n) with those of finite orthogonal and symplectic groups.
