## Representations of compact groups [MA5054]

### Sommersemester 2015

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

**Lecture**: |
Tuesday 2:15pm – 3:45pm, room 02.04.011 (room code M9/M10 5604.02.011) |
Anmeldung |

**Exercises**: |
Monday 8:30am - 10:00am, room 03.10.011 (room code M5 5610.03.011) |
Anmeldung |

### News

- The (oral) exam will take place on Wednesday, August 5. Location: Seminarraum (M5) (5610.03.011)
- Exam time slots: Doodle poll results.
- There will be no lecture on July 7. Instead, we'll have a lecture on Monday June 8, 8:30am - 10:00am (same room as above).
- The next exercise class will be on Monday June 15 (assignment 5).
- Exercise classes will take place once every two weeks (location/time: scheduled for Monday, 8:30am-10:00am based on the doodle poll).

### 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.

### 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)

In addition, I will provide handwritten notes: (

everything so far in one file )

### Exercises

### Other comments

You may be interested in the course Analysis on Groups, taught concurrently by Dr. Dominik Juestel. It will have some overlap with this course.
See here:

http://www-m7.ma.tum.de/bin/view/Analysis/AoG15#WikiVorlesung