NMAK14021U Representation theory (RepTh)

Volume 2014/2015
Education
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
Content

The main emphasis will be on finite dimensional complex representations of
linear groups, and infinite dimensional representations will only rarely be
discussed.

Fundamental results such as Schur's Lemma and  Mascheke'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
(linear) 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 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 as well as translate between different ways of describing
representations.

Competencies: The participants will be able to understand and use
representation theory where ever 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
  • Category
  • Hours
  • Exam
  • 60
  • Exercises
  • 16
  • Lectures
  • 32
  • Preparation
  • 98
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment, 9 weeks
3 mandatory assignments which must be handed in and passed individually. The first two 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.