NMAK14021U Representation theory (RepTh)
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
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.
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.
- Category
- Hours
- Exam
- 60
- Exercises
- 16
- Lectures
- 32
- Preparation
- 98
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessment, 9 weeks3 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.
Course information
- Language
- English
- Course code
- NMAK14021U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- A (Tues 8-12 + Thurs 8-17)
- Course capacity
- no limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Hans Plesner Jakobsen (8-6d646e7265766871437064776b316e7831676e)
Phone: +45 353-20689