Introduction to Chevalley groups and Bruhat-Tits theory

任课教师 Speaker:许俊彦
时间 Time: 每周一、周三 13:30-15:05 2020-9-14 ~ 9-16;10-5 ~ 12-16
地点 Venue:西楼第一会议室

课程描述 Description

Let k be a field and G a connected split semisimple algebraic group defined over k. The group of rational points G(k) (e.g., SL_n(C), SL_n(Q), SL_n(F_p)) is called a Chevalley group. Chevalley groups admit explicit generators and relations, which has many interesting applications including the constructions of finite simple groups (of Lie type) and maximal compact subgroups of G(k) when k is a local field (by Iwahori and Matsumoto). The latter construction is a precursor of Bruhat-Tits theory. This course is an introduction to this area of mathematics and the main reference is Steinberg’s lectures on Chevalley groups.

预备知识 Prerequisites

Theory of complex semisimple Lie algebra.

参考资料 References

1.     Representation theory, Fulton and Harris

2.     Lectures on Chevalley groups, Steinberg

3.     Linear algebraic groups, Borel

4.     Reductive groups over local fields, Tits.

5.     The Bruhat-Tits building of a p-adic Chevalley group and an application to representation theory