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数学学科2024系列学术报告之一

来源:理学院 发布日期:2024-01-03

  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。