Lie groups and representation theory
Summer term 2024, University of Regensburg
Summer term 2024, University of Regensburg
We will give an introduction to the theory of compact Lie groups and their representations, following the book Representations of compact Lie groups by Bröcker and tom Dieck. Particular theorems we will discuss are the Peter-Weyl theorem, which implies that every compact Lie group is a subgroup of a matrix group, and the Conjugation Theorem, which says that every Lie group admits up to conjugation a unique maximal torus. Finally, we will discuss the classification of connected compact Lie groups in terms of root systems.
Lectures: Monday, 10:15-11:45, M104 and Wednesday, 12:15-13:45, M101.
Exercise sessions: Friday, 14:15-15:45, M101.
There are lecture notes for the course, which will be expanded over time as the course progresses.
For more information about the course, including exercise sheets, see the corresponding GRIPS-page.