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401-4202-11L 9 Credits BSC , MSC D-MATH
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Representation Theory

Lecturers & Examiners: Prof. Dr. Emmanuel Kowalski
VVZ CR n/a

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)

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
  • Mon 14:15-16:00 (HG D 1.1)
  • Thu 08:15-10:00 (HG D 1.1)
4 h weekly
exercise Representation Theory
  • Thu 13:15-14:00 (HG E 1.2)
1 h weekly

Offered In