MATH 6500: Lie Groups (Spring 2012)

Instructor: Allen Knutson

This will be a first class on Lie groups and their representation theory. Not much is assumed beyond differential topology.

The basic plan:

1. A whirlwind passage through finite groups and their character theory.
2. Representations of tori.
3. Weight diagrams, and representations of U(n).
4. Weyl groups.
5. Root systems, and their classification.
6. Classification of irreducible representations of compact groups.
7. The Weyl character formula.