NMAK18005U Introduction to Representation Theory

Volume 2021/2022

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject


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)

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.


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.
4 hours lectures and 2 hours problem sessions in 9 weeks
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 92
  • Theory exercises
  • 18
  • Exam
  • 60
  • Total
  • 206
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.
Exam registration requirements






All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.

30 minute oral exam with 30 minutes preparation time. All aids allowed during the preparation time. No aids allowed during the examination.



Criteria for exam assesment

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