报告题目: Quantum linear supergroups and the Mullineux conjecture
The Mullineux conjecture is about computing the p-regular partition associated with the tensor product of an irreducible representation of a symmetric group with the sign representation. Since being formulated in 1979, the conjecture attracted a lot of attention and was not settled until 1997 when B. Ford and A. Kleshchev first proved it in a paper over a hundred pages. The proof was soon been shorten and, at the same time, its quantum version was also settled. The main ingredient of the proof is the modular branching rules.
In 2003, J. Brundan and J. Kujawa discovered a proof using naturally representations of the general linear supergroup. I am going to talk about how to use the quantum linear supergroup to resolve the quantum Mullineux conjecture. This is joint work with Yanan Lin and Zhongguo Zhou.
报告人概况： 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80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。