Winter 23/24  Representation Theory II  Spaces In Geometric Representation Theory
This is the course website for the lecture course Representation Theory II in Winter 2023/24.
Content
We study the geometry of some spaces that play an important role in the (geometric) representation theory of complex reductive groups and Lie algebras.
The course is about the classification, structure and representation theory of complex reductive algebraic groups. We focus on the geometry of flag varieties and related spaces, with a special attention to Schubert varieties.
Prerequisites
 Algebra I & II
 knowledge of representation theory of groups and Lie algebras, as well as structure theory of semisimple Liealgebras/groups (familiarity with representation theory is expected, not just the classification theorems)
 basic knowledge in algebraic geometry, for example, of projective complex varieties
Lecture Notes
Preliminary lecture notes can be found here.
Sources
Some sources that the course is based on:

Classification des groupes de Lie algébriques. Séminaire Claude Chevalley 19561958. Tomes 1, 2

Schémas En Groupes (SGA3)

Linear Algebraic Groups, James E. Humphreys,

Linear Algebraic Groups, Armand Borel,

Introduction to Actions of Algebraic Groups, Michel Brion,

Representations of Algebraic Groups, Jens Carsten Jantzen,

Representation Theory and Complex Geometry, Neil Chriss , Victor Ginzburg

A Very Simple Proof of Bott's Theorem, Michel Demazure,

Schubert varieties and Demazure's character formula, H. H. Andersen.
Schedule
Lectures
There are two lectures per week:
Wednesday 1012, Room: Großer Hörsaal,
Friday 1214, Room: Zeichensaal.
Problem session
Additionally, there will be a problem session:
Wednesday 1416, Room: 0.006.
Homework
There will be exercise problems posed in the lectures.
Everyone is encouraged to present their solutions on the blackboard during the problem session. You should do this at least once.
Exams
There will be an oral exam at the end of the semester. More information on the dates will follow.