时间 Time： 每周一、周三 13:30-15:05 2020-9-14 ~ 9-16；10-5 ~ 12-16
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.
of complex semisimple Lie algebra.
1. Representation theory, Fulton and
2. Lectures on Chevalley groups, Steinberg
3. Linear algebraic groups, Borel
4. Reductive groups over local
Bruhat-Tits building of a p-adic Chevalley group
and an application to representation theory