NMAK14021U Representation theory (RepTh)
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.
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
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.
- 7,5 ECTS
- Type of assessment
- Continuous assessment, 9 weeks6 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.
- 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.