Faculty of Science

Introduction to Representation Theory
Provider: Faculty of Science

Activity no.: 5571-23-07-31
	Enrollment deadline: 01/02/2023

Place

Department of Mathematical Sciences

Date and time

06.02.2023, at: 08:00 - 14.04.2023, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Jasmin Matz E-mail address: matz@math.ku.dk

Written language

English

Teaching language

English

Semester/Block

Block 3

Scheme group

A (Tues 8-12 + Thurs 8-17)

Exam form

Continuous assessment

Exam details

Two 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 aids

All aids allowed

Grading scale

7 point grading scale. For PhD students: Passed / Not Passed

Course workload

Course workload category	Hours
Exam	60.00
Course Preparation	92.00
Lectures	36.00
Theory exercises	18.00

Sum	206.00

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

Click the search button to search Courses.

See which courses you can attend and when

Jan	Feb	Mar	Apr
May	Jun	Jul	Aug
Sep	Oct	Nov	Dec