報告題目：Multiplication formulas in the queer q-Schur superalgebras

　　報告人：杜杰，新南威爾士大學教授

　　時間：2024年1月6日(星期六）10:00-11:00

　　地點：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.

　　報告人簡介：

　　杜杰，澳大利亞新南威爾士大學教授，在Weyl群的胞腔分解、代數(shù)群，q-Schur代數(shù)、Ringel-Hall代數(shù)及量子群和量子超群等方面取得了一系列原創(chuàng)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.等國際著名數(shù)學學術雜志上發(fā)表科研論文100余篇，與合作者編著專著2本，分別由美國數(shù)學會和倫敦數(shù)學會發(fā)表。 擔任多個數(shù)學類學術雜志編委。作為項目負責人多次獲得澳大利亞基金委的資助。