NMAK18005U Introduction to Representation Theory
MSc Programme in Mathematics
MSc Programme in Mathematics w. a minor subject
The main emphasis will be on finite dimensional complex representations of linear groups, but infinite dimensional representations of specific groups will also be discussed.
We begin with fundamental results such as Schur's Lemma and Mascheke's Theorem. Fundamental constructions such as tensor product representations and dual (contragredient) are then discussed.
The first major topic is compact groups culminating with a proof of the Peter - Weyl Theorem. The Haar measure will be mentioned and the Lie algebra of a linear group will be discussed. Time permitting we will then discuss finite-dimensional as well as infinite dimensional representations of specific Lie groups.
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.
- 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
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.
- Theory exercises