中科院数学与系统科学研究院
数学研究所
表示论研讨班
报告人：李鹏程 博士（北京大学）
题 目：Categorical Actions and Derived Equivalences for Finite Odd-dimensional Orthogonal Groups
时 间：2021.11.25（星期四），14:30-17:00
2021.12.02（星期四），14:30-17:00
地 点：数学院南楼N802
摘 要：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.
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