# Representation theory I

This page contains the information about the course **V4A3 Representation Theory I**, taught by prof. dr. Catharina Stroppel.

In this course we will study complex semisimple Lie algebras, their classification and their representation theory.

Lie algebras arise naturally as tangent spaces of Lie groups or affine algebraic groups. Their representation theory is a model for many other — often more complicated and more involved — structures in representation theory. We in particular will learn the concept of (highest) weight theory and the basic concepts of reflection groups. The first part will follow standard literature like [H], [K]. The second part will be on root systems, integrality questions and Chevalley groups. If time allows we will finally deal with the famous category O of infinite dimensional highest weight modules.

**Prerequisites** Good knowledge of basics in algebra is absolutely necessary. Some knowledge of Lie groups or affine algebraic groups will be useful for the second part.

## Exam

- Monday, July 17 2019, 9–11, Großer Hörsaal
- Friday, September 20 2019, 9–11, Kleiner Hörsaal

## References

[H] J, Humphreys, Introduction to Lie algebras and representation theory. Graduate Texts in Mathematics, 9, Springer 1978.

[K] A. Knapp, Lie groups beyond an introduction. Progress in Mathematics, 140. Birkhäuser 2002.