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.
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。