# 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 Lie-algebras/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 1956-1958. 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 10-12, Room: Großer Hörsaal,
Friday 12-14, Room: Zeichensaal.

### Problem session

Additionally, there will be a problem session:

Wednesday 14-16, 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.