报告题目：Presenting hyperoctahedral q-Schur algebras
报告人：Du Jie（新南威尔士大学）
报告时间：6月1日10：00-11：00
报告地点：理学院1-301
报告摘要：The family of q-Schur algebras consists of fundamental objects in Lie theory and representation theory. This family has grown from the first class of q-Schur algebras of type A, introduced in 1980s, to now eight classes, including the class of hyperoctahedral q-Schur algebras. Various q-Schur algebras link representations of the corresponding quantum groups with those of associated Hecke algebras and, in some cases, with those of finite groups of Lie type. They also play important role in new realizations of quantum groups via Hecke algebras. q-Schur algebras are endomorphism algebras of some Hecke algebra modules. Near the end of the last century, Doty-Giaquinto initiated a program for finding presentation of q-Schur algebras (of type A). Since then, this program has been extended to other classes in the family, including affine q-Schur algebra by McGerty, Deng-D.-Fu and q-Schur superalgebras by El Hussain-Kujawa.
In this talk, I will report on a recent progress on the presentation problem for q-Schur algebras arising from the i-quantum groups U^j(n) and U^i(n), the latter is also known as hyperoctahedral q-Schur algebras. Note that the i-quantum group case is much more complicated since the relations involve not only diagonal relations but also tridiagonal relations. This is joint work with Jian Chen.
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。 相关成果发表在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100余篇，与合作者编写专著2部，分别由美国数学会和伦敦数学会发表，曾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。
