Deligne--Lusztig constructions over finite fields and finite rings III

：陈哲（汕头大学）
：2022-06-10 15:00
：腾讯会议ID：43657423564（无密码）

报告人：陈哲（汕头大学）

时  间：6月10日下午15:00

地  点：腾讯会议ID：43657423564（无密码）

内容摘要:

This is a series of three lectures.

(I) In the first talk I would like to give an introduction to Deligne--Lusztig theory of reductive groups over finite fields, with a focus on the case of SL_2(F_q). Time permitting, I will also discuss some basics of the generalisation for reductive groups over discrete valuation rings (called higher Deligne--Lusztig theory).

(II) In the second talk, I would like to discuss the algebraisation problem of higher Deligne--Lusztig representations raised by Lusztig, which seeks algebraic realisations (via, say, Clifford theory) of these geometrically constructed representations. I will discuss our resolution of this problem at even levels in a joint work with Stasinski in 2017, as well as our recent progress towards the odd level case.

(III) In the third talk, I plan to discuss a curious restriction-to-torus formula of Deligne--Lusztig characters, which is motivated by a phenomenon appeared in the algebraisation problem and by a work of Reeder.

个人简介：

陈哲，汕头大学讲师，2017年博士毕业于Durham University。目前研究围绕在李型群的表示论及相关的几何构造，研究工作发表在IMRN、Math Ann、Selecta Math等期刊。

 

联系人：余世霖