Introduction to Representation Theory
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
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.
- 7,5 ECTS
- Type of assessment
- Type of assessment details
- Continuous assessment
Two assignments which must be handed in individually which count 50% towards the final grade and a final oral exam of 25 min. without preparation which counts 50% 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)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 3
- No limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Jasmin Matz (4-6f63767c426f63766a306d7730666d)
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Courseinformation of students