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Representation Theory
Last Updated: 2026-06-03 00:07:54
Abstract
This course offers an introduction to the representation theory of finite groups. The idea of representation theory is to study groups via their actions on finite-dimensional vector spaces. This is a very powerful idea, since it reduces many group-theoretic problems to problems in linear algebra. Representation theory has far-reaching applications in many different fields.
Objective
The goal of the course is to present the basic ideas and concepts of the representation theory of finite groups, together with many explicit examples and some important applications. The student will then be able to apply the basic theory both to theoretical questions and to explicit examples, and will be ready to study other aspects of representation theory not covered during the class, using the intuition and knowledge presented during the lectures (for instance, the general representation theory of reductive groups).
Content
The planned course outline is as follows: - basic definitions and motivating examples - complete reducibility, Schur’s lemma - tensor products of representations - character tables, examples - induced representations, Frobenius reciprocity - Mackey theory - Burnside’s theorem
Resources
Lecture Notes
The lecture notes for a previous version of the course will be made available on the course website after each lecture.
Literature
J-P. Serre: "Linear representations of finite groups", Springer GTM, vol 42. W. Fulton and J. Harris: "Representation theory. A first course", Springer GTM/Readings in Mathematics. A.W. Knapp: "Representation Theory of Semisimple Groups: An Overview Based on Examples", Princeton. H. Weyl: "The theory of groups and quantum mechanics", Dover. E. Kowalski: "An introduction to the representation theory of groups", AMS Graduate Texts in Math., 2014.
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Representation Theory | No time listed | 2 h weekly |
| exercise | Representation Theory | No time listed | 0.5 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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