NMAK14021U  Representation theory (RepTh)

Volume 2015/2016
Education
MSc Programme in Mathematics
Content

The main emphasis will be on finite-dimensional complex representations of finite and compact groups. Some time will be devoted to examples important in applications, such as abelian groups (signal processing) and the symmetric group (combinatorics.)

Fundamental results such as Schur's Lemma and  Maschke's Theorem, as well as fundamental structures such as tensor products and dual vector spaces will be covered. The first major result will be the Peter - Weyl Theorem for compact groups. The Haar measure will be mentioned and likewise the Lie algebra of a linear group will be discussed. The second major result will be the description of irreducible representations in terms of highest weights. This will be covered at least for certain Lie groups and Lie algebras.

Learning Outcome

Knowledge: The student will acquire a working 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 as well as translate between different ways of describing
representations.

Competencies: The participants will be able to understand and use representation theory wherever they may encounter it. They will also be able to construct representations of given groups.

4 hours lectures and 2 hours problem sessions in 8 weeks
Credit
7,5 ECTS
Type of assessment
Continuous assessment, 9 weeks
6 mandatory homework assignments which must be handed in and passed individually. The first assignment can be resubmitted once.
Marking scale
passed/not passed
Censorship form
No external censorship
One internal examiner.
Re-exam
30 minute oral exam with 30 minutes preparation time. All aids allowed during the examination 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
  • Exercises
  • 16
  • Exam
  • 60
  • Total
  • 206