# Representation theory of finite groups

• Lecturer: Arthur Bik
• Date: Thursdays 7:30-9:00 and Fridays 9:15-10:45
• Room: SG 3-10
• Keywords: Representation theory, Group actions, Characters
• Prerequisites: Basic knowledge about groups and vector spaces
• Remarks: https://personal-homepages.mis.mpg.de/arbik/reptheory22.html

## Abstract

Representation theory is about understanding and exploiting symmetry using linear algebra. The central objects of study are linear actions of groups on vector spaces. This gives rise to a very structured and beautiful theory. The aim of this course dealing with finite groups and complex vector spaces is to introduce this theory. Representation theory plays a major role in mathematics and physics. For example, it provides a framework for understanding finite groups, special functions, and Lie groups and algebras. In number theory, Galois groups are studied via their representations; this is closely related to modular forms. In physics, representation theory is the mathematical basis for the theory of elementary particles. After introducing the concept of a representation of a group, we will study decompositions of representations into irreducible constituents. A finite group only has finitely many distinct irreducible representations; these are encoded in a matrix called the character table of the group. One of the goals of this course is to use representation theory to prove Burnside's theorem on solvability of groups whose order is divisible by at most two prime numbers. Another goal is to construct all irreducible representations of the symmetric group.

To keep informed about changes to this lecture subscribe to lecture mailinglist

### Important information

• Due to the pandemic, it is strongly recommended to register for a lecture series before attending one of the lectures. For this registration, we simply use the mailing list for the lecture series. So, if you plan to attend a lecture (series), please subscribe the mailing list which is linked below the respective lecture.
• Obviously, this rule is only valid for in-person lectures. However, even for the online events it might be a good idea to subscribe. This way, you will receive the information on how to attend the online meetings.

## Access Information (presence lectures only)

External guests please use the main entry Inselstr. 22 and go to the 3rd. floor (reception, see the map). All other doors are closed.

23.05.2022, 02:30