Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups

发布时间：2021-11-29 作者：浏览次数：

Speaker:	李鹏程	DateTime:	2021年12月1日（周三）上午9:30-11:30和12月8日（周三）上午9:30-11:30
Brief Introduction to Speaker: 李鹏程，北京大学博士。		Place:	腾讯会议号：874-7362-4450
Abstract:In this paper we prove that Broue's abelian defect group conjecture is true for the finite odd-dimensional orthogonal groups SO2n+1(q), with q odd, at odd linear primes. We frist 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 SO2n+1(q) in non-defining characteristic, by extending the corresponding work of Dudas-Varagnolo-Vasserot for unipotent representations. To obtain derived equivalences of blocks and their Brauer correspondents, we turn to investigate a special kind of blocks, called isolated Rouquier blocks. Finally, the desired derived equivalence is guaranteed by the work of Chuang-Rouquier showing that categorical actions provide derived equivalences between weight spaces, which are exactly the isolated-blocks in our situation. This is a joint work with Yanjun Liu and Jiping Zhang.