Introduction to Representation Theory

Course content

The main emphasis will be on finite dimensional complex representations of linear groups. Topics include:

Basic definitions and properties of representations, including Schur's Lemma and Maschke's Theorem.

The representation theory of finite groups, including Schur orthogonality.

Fundamental constructions such as tensor product, dual representations and induced representations.

Representation theory of compact groups, including the Peter-Weyl Theorem.

Description of the irreducible representations of S_n, SU(2), SO(3), and sl(2,C)


MSc Programme in Mathematics
MSc Programme in Mathematics with 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 9 weeks

Example of course literature

Ernest B. Vinberg: Linear Representations of Groups.



Basic group theory, measure theory, and advanced linear algebra, e.g., from the following courses:

Algebra 2 (Alg2),
Lebesgueintegralet og målteori (LIM) - alternatively Analyse 2 (An2) from previous years
Advanced Vector Spaces (AdVec).

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course of the semester
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
One internal examiner.
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
  • Lectures
  • 36
  • Preparation
  • 92
  • Theory exercises
  • 18
  • Exam
  • 60
  • English
  • 206