NMAK18005U Introduction to Representation Theory
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
The main emphasis will be on finite dimensional complex representations of linear groups. Topics include:
Basic definitions and properties of representations, including Schur's Lemma and Maschke's Theorem.
The representation theory of finite groups, including Schur orthogonality.
Fundamental constructions such as tensor product, dual representations and induced representations.
Representation theory of compact groups, including the Peter-Weyl Theorem.
Description of the irreducible representations of S_n, SU(2), SO(3), and sl(2,C)
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.
Algebra 2 (Alg2),
Lebesgueintegralet og målteori (LIM) - alternatively Analyse 2 (An2) from previous years
Advanced Vector Spaces (AdVec).
Academic qualifications equivalent to a BSc degree is recommended.
- Category
- Hours
- Lectures
- 36
- Preparation
- 92
- Theory exercises
- 18
- Exam
- 60
- Total
- 206
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessmentOral examination, 25 min
- Type of assessment details
- Continuous assessment
Oral examination 25 minutes without preparation.
Two assignments which must be handed in individually and a final oral exam of 25 min. without preparation. The oral exam and the homework assignments each account for 50%. The final oral needs to be passed in order to pass the course. - Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner.
- 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 should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Course information
- Language
- English
- Course code
- NMAK18005U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 3
- Schedule
- A
- Course capacity
- No limit
The number of seats may be reduced in the late registration period
Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Jasmin Matz (matz@math.ku.dk)
- Dani Tove Kaufman (dk@math.ku.dk)