NMAK18005U Introduction to Representation Theory
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)
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.
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.
- Theory exercises
- 7,5 ECTS
- Type of assessment
- Continuous assessmentThree 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.