Introduction to Representation Theory

Course content

The main emphasis will be on finite dimensional complex representations of linear groups, but infinite dimensional representations of specific groups will also be discussed. 

We begin with fundamental results such as Schur's Lemma and Mascheke's Theorem. Fundamental constructions such as tensor product representations  and dual (contragredient) are then discussed. 

The first major topic is compact groups culminating with a proof of the Peter - Weyl Theorem. The Haar measure will be mentioned and the Lie algebra of a linear group will be discussed. Time permitting we will then discuss finite-dimensional as well as infinite dimensional representations of specific Lie groups.


MSc Programme in Mathematics

MSc Programme in Mathematics w. a minor subject

Learning outcome

Knowledge: The student will get a knowledge of the most fundamental theorems and constructions in this area.


Skills: It is the intention that the students get a "hands on'' familiarity  with the topics so that they can work and study specific representations of specific groups while at the same time learning the abstract framework.

Competencies: The participants will be able to understand and use representation theory wherever they may encounter it. They will know important examples and will be able to construct  representations of given groups.


4 hours lectures and 2 hours problem sessions in 8 weeks

Example of course literature

Ernest B. Vinberg: Linear Representations of Groups.



7,5 ECTS
Type of assessment
Continuous assessment
Three assignments which must be handed in individually. The first two count 30% each and the third counts 40% towards the final grade.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.


Single subject courses (day)

  • Category
  • Hours
  • Preparation
  • 98
  • Lectures
  • 32
  • Theory exercises
  • 16
  • Exam
  • 60
  • English
  • 206