题    目：Finite dimensional algebras and quantum groups

主讲人：杜杰 教授

单    位：澳大利亚新南威尔士大学

时    间：2025年6月12日 14:30

地    点：学院一楼报告厅

摘    要：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.

简    介：杜杰，澳大利亚新南威尔士大学教授。长期从事代数群、李代数和量子群及其表示论等相关前沿理论的研究，引进了许多解决复杂问题的新思想和新方法，开创了一些新的研究领域，在有限李型群结构及其表示理论、量子Schur-Weyl对偶理论、箭图和拟遗传代数表示理论等代数前沿领域的研究均取得了突出的原创新成果。 杜杰教授与其合作者联合出版了专著《Finite dimensional algebras and quantum groups》（美国数学会出版社，759页）、《A double Hall algebra approach to affine quantum Schur-Weyl theory》(剑桥大学出版社，210页），在Adv. Math.，Trans. Amer. Math. Soc.，J. Reine Angew. Math.，Comm. Math. Phys.，J. London Math. Soc.，Math. Z，Proc. London Math. Soc.，Int. Math. Res. Not.，J. Algebra等国际著名数学期刊发表学术论文90余篇。