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Introduction to Representation Theory
Provider: Faculty of Science

Activity no.: 5571-23-07-31 
Enrollment deadline: 01/02/2023
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time06.02.2023, at: 08:00 - 14.04.2023, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserJasmin Matz    E-mail address: matz@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 3
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam formContinuous assessment
Exam detailsTwo assignments which must be handed in individually which count 50% towards the final grade and a final oral exam of 25 min. without preparation which counts 50% towards the final grade
Exam aidsAll aids allowed
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Exam60.00
Course Preparation92.00
Lectures36.00
Theory exercises18.00
Sum206.00
Content
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)

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 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.

Literature
Example of course literature:
Ernest B. Vinberg: Linear Representations of Groups.

Teaching and learning methods
4 hours lectures and 2 hours problem sessions in 9 weeks

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