数学学科2024系列学术报告之一

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

　　报告人：杜杰，新南威尔士大学教授

　　时间：2024年1月6日(星期六）10:00-11:00

　　地点：1-301

　　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.

　　报告人简介：

　　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、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， 目前在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发表科研论文100余篇，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。