报告题目：Multiplication formulas in the queer q-Schur superalgebras

报告人：杜杰教授 (University of New South Wales, Australia)

时间：2024年01月12日（周五）下午16:00-17:00    

地点：理科楼数学系A304

报告摘要：By the super version of Wedderburn’s Theorem, a finite dimensional complex simple (associative) superalgebras is isomorphic to either a (full) matrix            superalgebra or a queer matrix superalgebra. This gives rise to two series of Lie superalgebras: the general linear Lie superalgebra and the queer Lie superalgebra.         Thus, there are naturally two super versions of the Schur-Weyl duality, two types of Schur superalgebras, and their quantum analogues.

In this talk, I am going to introduce the queer q-Schur superalgebras associated with the quantum queer supergroup and to discuss their fundamental structure,            including their standard bases and some fundamental multiplication formulas. These formulas are the keys to a new construction of the quantum queer supergroup      and are obtained from certain commutation relations in Hecke-Clifford superalgebras. If time permits, the Schur-Weyl-Olshanski duality at the integral level will also     be  discussed.

 This is joint work with H. Gu, Z. Li, and J. Wan.

报告人简介：杜杰，澳大利亚新南威尔士大学教授。1987年在华东师范大学获得博士学位。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., J. Reine Angew. Math., Proc. London Math. Soc., Trans. Amer. Math. Soc., Comm. Math. Phys., Int. Math. Res. Not., Math. Z. 等国际著名数学学术期刊上。与合作者完成专著2本，分别由美国数学会和伦敦数学会出版。担任多个数学类学术期刊编委。作为项目负责人多次获得澳大利亚国家基金委的资助。

邀请人：邓邦明