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Representation Theory
Last Updated: 2026-06-01 11:31:23
Abstract
The ideas of representation theory are among the most important unifying concepts in current mathematical research, and they are relevant to extremely diverse fields, from geometry and quantum mechanics to number theory, besides being an extremely important subject by itself. The course will present an introduction to various aspects of the representation theory of groups.
Objective
The goal of the course is to present the basic ideas and concepts of the representation theory of groups, together with examples of some of its important applications. The student will then be able to apply these basic facts, 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, or more sophisticated applications in physics).
Content
The planned course outline is as follows: * Introduction and motivation with some simple examples * Abstract representation theory of groups, including e.g. induced representations, Burnside's irreducibility criterion, etc * Representations of finite groups in characteristic zero * Examples and sample applications (e.g., Burnside's theorem on groups of order divisible by at most two primes) * Representations of compact groups and applications * Introduction to the representations of locally-compact, non-compact, groups through the example of SL(2,R)
Resources
Lecture Notes
The lecture notes for a previous version of the course will be made available.
Literature
E. Kowalski: "An introduction to the representation theory of groups", AMS Graduate Texts in Math., 2014. 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
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Representation Theory |
|
4 h weekly |
| exercise | Representation Theory |
|
1 h weekly |
Offered In
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Wahlfächer (Für das Master-Diplom in Angewandter Mathematik ist die folgende Zusatzbedingung (nicht in myStudies ersichtlich) zu beachten: Mindestens 14 KP der erforderlichen 26 KP aus Kern- und Wahlfächern müssen aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten stammen.)
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