Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups
数学专题报告
报告题目(Title)：Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups
报告人(Speaker)：李鹏程（清华大学）
地点(Place)：后主楼1223
时间(Time)：2023年9月26日（周二）15:00-15:50
邀请人(Inviter)：肖杰
报告摘要
In this talk, I will give a brief introduction to Kac-Moody categorification and Broue's abelian defect group conjecture. We prove that Broue's abelian defect group conjecture is true for the finite odd-dimensional orthogonal groups SO_{2n+1}(q) at linear primes with q odd. We firstly make use of the reduction theorem of Bonnafe-Dat-Rouquier to reduce the problem to isolated blocks. Then we construct a categorical action of a Kac-Moody algebra on the category of quadratic unipotent representations of the various groups SO_{2n+1}(q) in non-defining characteristic, by generalizing the corresponding work of Dudas-Varagnolo-Vasserot for unipotent representations. This is one of the main ingredients of our work which may be of independent interest. To obtain derived equivalences of blocks and their Brauer correspondents, we define and investigate isolated RoCK blocks. Finally, we establish the desired derived equivalence based on the work of Chuang-Rouquier that categorical actions provide derived equivalences between certain weight spaces. This is a joint work with Yanjun Liu and Jiping Zhang.
组织者：肖杰、方杰鹏、兰亦心
