The i-quantum groups Uȷ (n) and Uı (n)

：杜杰（澳大利亚新南威尔士大学）
：2023-08-19 16:00
：厦门大学海韵园实验楼105报告厅

报 告 人：杜杰（澳大利亚新南威尔士大学）

时  间：2023年8月19日16:00

地  点：海韵园实验楼105报告厅

内容摘要:

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 ȷ (n) and U ı (n) and their associated q-Schur algebras S ȷ (n, r) and S ı (n, r) of types B and C, respectively. This includes short (element) multiplication formulas, long (element) multiplication formulas, and triangular relations in S ȷ (n, r) and S ı (n, r). We will also give realisations of Beilinson–Lusztig–MacPherson type for both U ȷ (n) and U ı (n) and discuss their Lusztig forms. This allows us to link representations of U ȷ (n) and U ı (n) with those of finite orthogonal and symplectic groups.

个人简介：

杜杰，澳大利亚新南威尔士大学教授。在Weyl群的胞腔分解、代数群，q-Schur代数及其表示、在Ringle-Hall 代数及量子群和量子超群等方面取得了一系列原创性的成果，目前已经在国际一流杂志发表论文70余篇，合作完成专著《Finite dimensional algebras and quantum groups》和《A double Hall algebra approach to quantum affine Schur-Weyl theory》,分别在美国数学会和伦敦数学会出版。

 

 

联系人：林亚南