## Representations of compact groups [MA5054]

### Sommersemester 2021

**Lecturer**: |
Prof. Dr. Robert König |

**Assistants**: |
Farzin Salek, Zahra Khanian |

**Lecture**: |
Thursdays 4:15pm – 5:45pm (zoom) |

**Exercises**: |
Fridays 4:00pm - 5:30pm (zoom) |

### News

There will be no lecture on May 13 (holiday). The exercises on Friday the 14th will take place as usual.

### Contents

This course will serve as an introduction to the theory of Lie groups and their representations, a topic of central importance in physics. Subjects to be covered include:

- Lie groups and algebras, the exponential map
- Peter-Weyl theorem
- maximal tori, roots and weights
- the Weyl group, the Weyl character formula and representations of the classical groups.

In addition, some applications to physics may be discussed.

### Exercises

### Literature

There are plenty of excellent textbooks on these topics. The lectures will follow the second half of

- B. Simon, Representation of finite and compact groups, AMS (1996)

to a large extent. Other recommended literature (more may be provided during the course):

- A. Knapp, Lie groups beyond an introduction, Birkhaeuser (1996)
- R. Goodman and N. Wallach, Representations and Invariants of the Classical Groups, Cambridge University Press (1998)
- T. Broeckner and T. Dieck, Representations of Compact Lie Groups, Springer (1985)

### Some notes

Continuously updated (partial)

lecture notes/summary.