NMAK18005U  Introduction to Representation Theory

Volume 2018/2019
Education

MSc Programme in Mathematics

MSc Programme in Mathematics w. a minor subject

Content

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.

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.

 

 

4 hours lectures and 2 hours problem sessions in 8 weeks
Written
Individual
Credit
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

 

 

 

 

 

Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Re-exam

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.

 

  • Category
  • Hours
  • Preparation
  • 98
  • Lectures
  • 32
  • Theory exercises
  • 16
  • Exam
  • 60
  • Total
  • 206