Introduction to Deligne-Lusztig theory through the example of SL(2,q)

Cédric Bonnafé

(CNRS)

Cédric Bonnafé is a senior researcher of French National Scientific Research Center (CNRS), working at Université Montpellier. He is an expert in representation theory of finite reductive groups and related objects (such as Hecke algebras or rational Cherednik algebras). He made important contributions to the Kazhdan-Lusztig theory of cells, the study of Deligne-Lusztig varieties and related topics.

For more information, you are welcome to visit his home page: https://imag.umontpellier.fr/~bonnafe/index-anglais.html

Time

Mon., 15:20-16:55 &

Wed., 19:20-20:55

Oct. 9-Oct. 30, 2024

(excluding Oct. 28)

Venue

Lecture Hall C548

Shuangqing Complex Building A

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).

注：本课程面向学习过基本表示论知识的本科生和研究生。

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