Note: There is no lecture on Dec.16,2022. The course will continue on Dec.21, Dec.23,2022.

Course Description:  

Deligne-Lusztig theory aims to provide geometric methods (l-adic cohomology of varieties in positive characteristic) to study representations of finite groups of Lie type. We propose an introduction to this theory, starting with the enlightening example of the finite group SL_2(q) acting on Drinfeld curve. In the second part of this course, we will develop the general theory as well as some important remaining problems. If time permits, we will also discuss representations in positive characteristic or action of braid groups on the cohomology of Deligne-Lusztig varieties.

Lecturer:

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.

Notes：

lecture-1.pdf

lecture-2.pdf

lecture-3.pdf

lecture-4.pdf

lecture-5-2.pdf

lecture-6.pdf

lecture-7.pdf

lecture-8.pdf

lecture-9.pdf

lecture-10.pdf 

lecture-11 2.pdf

lecture-12.pdf

lecture-13.pdf

Videos:

http://archive.ymsc.tsinghua.edu.cn/pacm_course?html=Introduction_to_Deligne-Lusztig_theory.html