Speaker：Zhe Chen（Shantou University）

Time：2022-06-10, 15:00

Location：Tencent Meeting ID：43657423564（No Password）

Abstract:

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.