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Introduction to Representation Theory
Provider: Faculty of Science

Activity no.: 5571-19-07-31 
Enrollment deadline: 04/02/2019
Tilmelding : Introduction to Representation Theory
ECTS credits7.50
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time04.02.2019, at: 09:00 -
07.04.2019, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserHans Plesner Jakobsen    E-mail address: jakobsen@math.ku.dk
Teaching languageEnglish partially in English
Semester/BlockBlock 3
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam formContinuous assessment
Exam formContinuous assessment
Exam detailsThree assignments which must be handed in individually. The first two count 30% each and the third counts 40% towards the final grade.
Course workload
Course workload categoryHours
Preparation98.00
Lectures32.00
Theory exercises16.00
Exam60.00
Sum206.00
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.

Teaching and learning methods
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.

Content
The main emphasis will be on finite dimensional complex representations of linear groups, but infinite dimensional representations of specific groups will also be discussed.

We begin with fundamental results such as Schur's Lemma and Mascheke's Theorem. Fundamental constructions such as tensor product representations and dual (contragredient) are then discussed.

The first major topic is compact groups culminating with a proof of the Peter - Weyl Theorem. The Haar measure will be mentioned and the Lie algebra of a linear group will be discussed. Time permitting we will then discuss finite-dimensional as well as infinite dimensional representations of specific Lie groups.

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