题目:The i-quantum groups U? (n) and U? (n)
报告人: 杜杰教授 (University of New South Wales, Australia)
报告时间:2024年1月19日上午10:00-11:00
报告地点:览秀楼105

摘要:When I. Schur used representations of the symmetric group  Sr to determine polynomial representations of the complex general linear group GLn(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 GLn(C) and Sr. 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 ? (n) and U ? (n) and their associated q-Schur algebras S ? (n, r) and S ? (n, r) of types B and C, respectively. This includes short (element) multiplication formulas, long (element) multiplication formulas, and triangular relations in S ? (n, r) and S ? (n, r). We will also give realisations of Beilinson–Lusztig–MacPherson type for both U ? (n) and U ? (n) and discuss their Lusztig forms. This allows us to link representations of U ? (n) and U ? (n) with those of finite orthogonal and symplectic groups.


邀请人:吕仁才