珠海数学杰出学者讲座第53讲-Finite dimensional algebras and quantum groups

讲座题目：Finite dimensional algebras and quantum groups
时间 Datetime:2025年11月13日，星期四，16:30-18:30
地点 Venue: 中大珠海校区海琴二号A412-1

主持人 Host：黄敏 副教授
报告人 Speaker: 杜杰 教授
单位 Affiliation: 新南威尔士大学
报告摘要 Abstract:
Using a geometric setting of q-Schur algebras, Beilinson-Lusztig-MacPherson discovered a new basis for quantum gl_n (i.e., the quantum enveloping algebra Uq(gl_n) of the Lie algebra gl_n) and its associated matrix representation of the regular module of Uq(gl_n). This beautiful work shows that the structure of the quantum linear group is hidden in the structure of Hecke algebras. The work has been generalized (either geometrically or algebraically) to quantum affine gl_n, quantum super gl_{m|n}, and recently, to some i-quantum groups of type AIII. (All were good PhD projects.) In this talk, I will report on a completion of the work for a new construction of the quantum queer supergroup using Hecke-Clifford superalgebras and their associated q-Schur superalgberas.
报告人简介：
杜杰，澳大利亚新南威尔士大学教授。 1982年1月苏州大学本科毕业, 1987年7月华东师范大学博士毕业。在Weyl群的胞腔分解、代数群，q-Schur代数、Ringel-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。 相关成果发表在Adv. Math., Comm. Math. Phys., Int. Math. Res. Not., J. Reine Angew. Math., Math. Z., Proc. London Math. Soc., Sci. China Math., Trans. Amer. Math. Soc.等国际著名数学学术杂志上。与合作者编著专著2本，分别由美国数学会和伦敦数学会发表。 担任多个数学类学术杂志编委。作为项目负责人多次获得澳大利亚基金委的资助。