数学学科2018系列学术报告之二十九

报告题目：Slim cyclotomic q-Schur algebras

报告人: 杜杰

时间：2018年12月29日，15:00--16:00

地点：1-232

摘要：Slim cyclotomic q-Schur algebras were first introduced by Z. Lin and H. Rui, as centralizer subalgebras of Dipper-James-Mathas’ cyclotomic q-Schur algebras. Recent developments allow us to take the investigation to a new level. First, by using the matrix labelling of C. Mak for certain double cosets, we may construct an integral basis, simpler than the cellular basis, for these algebras. Second, the introduction of the Lusztig type form for quantum affine gl_n by Q. Fu and myself allows us to establish the cyclotomic Schur-Weyl duality at the integral level. Finally, when q is not a root of unity, we obtain a classification of irreducible representations. I will also mention some problems and conjectures. This is joint work with B. Deng and G. Yang.

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代数及其表示、在Ringle-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，目前已经在国际一流杂志发表论文90余篇，合作完成专著《Finite dimensional algebras and quantum groups》和《A double Hall algebra approach to quantum affine Schur-Weyl theory》,分别在美国数学会和伦敦数学会出版。