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
Oral examination, 25 min
Type of assessment details
Continuous assessment
Oral examination 25 minutes without preparation.
Two assignments which must be handed in individually and a final oral exam of 25 min. without preparation. The oral exam and the homework assignments each account for 50%. The final oral needs to be passed in order to pass the course.
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 assessment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 92
  • Theory exercises
  • 18
  • Exam
  • 60
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 3
No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Jasmin Matz   (4-7064777d437064776b316e7831676e)
Saved on the 15-02-2024

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