题 目：Some new extensions of Hecke endomorphism algebras I
报告人： Leonard Scott (University of Virginia)
摘 要： This is the first of two talks by myself and Brian Parshall. It is based on our joint work with Jie Du, in progress. I will give some of the history and framework leading to the main conjecture we had made, asserting the existence of a kind of generalized q-Schur algebra, suitable for studying cross-characteristic representation theory of finite groups of Lie type. The conjecture is now a theorem, with some of its proof to be sketched in Parshall’s talk. I will mention some applications as time permits.
时 间：2018年7月5日 上午9:00
题 目： Some new extensions of Hecke endomorphism algebras, II
报告人： Brian Parshall (University of Virginia)
摘 要： This talk is joint work with Jie Du (UNSW) and Leonard Scott (UVA), in progress.
As is well-known, the (cross-characteristic) representation theory of the finite groups $GL_n(q)$ can be studied using the famous $q$-Schur algebra, which itself is realized as a Hecke endomorphism algebra. This talk concerns, for the other finite groups of Lie type, an enlargement of the $q$-Schur algebra, based on Kazhdan-Lusztig cell theory, and new ways to use it. In all types the algebra is stratified, and if the characteristic of the field $F_q$ is not a bad prime, it is quasi-hereditary. Interestingly, the proof of the main theorem is based in a non-trivial way on some new constructions of a categorical nature. The talk will be a continuation of Leonard Scott’s talk.
时 间：2018年7月5日 上午10:00
题 目： Quantum linear supergroups and the
报告人： Jie Du (University of New South Wales)
摘 要： 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.
时 间：2018年7月5日 上午11:00