Abstract:

Deligne-Lusztig theory stared in 1976 with the original paper by Deligne-Lusztig. It aims to use geometric methods and $l$-adic cohomology for studying representations of finite reductive groups (as GL(n,q), Sp(2n,q), SO(n,q),...). This course aims to introduce to this theory by investigating the example of SL(2,q): this example is small enough to allow to compute everything explicitly and rich enough to illustrate most of the subtle points of the theory. This course must be seen as a soft entry in the world of "geometric representation theory", a very active and competitive research field in mathematics.

This course requires only to know the basics of character theory of finite groups and basic algebraic geometry (for instance, the first chapter of Hartshorne's book, which deals with varieties over algebraically closed fields).

Registration: https://www.wjx.top/vm/w9usLgR.aspx#

注：面向学习过基本表示论知识的本科生和研究生。