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Darstellungstheorie kompakter Gruppen
Representations of Compact Groups

Modul MA5054

Dieses Modul wird durch Fakultät für Mathematik bereitgestellt.

Diese Modulbeschreibung enthält neben den eigentlichen Beschreibungen der Inhalte, Lernergebnisse, Lehr- und Lernmethoden und Prüfungsformen auch Verweise auf die aktuellen Lehrveranstaltungen und Termine für die Modulprüfung in den jeweiligen Abschnitten.


MA5054 ist ein Semestermodul in Englisch auf Master-Niveau das unregelmäßig angeboten wird.

Die Gültigkeit des Moduls ist von SS 2018 bis SS 2018.

GesamtaufwandPräsenzveranstaltungenUmfang (ECTS)
150 h 45 h 5 CP

Inhalte, Lernergebnisse und Voraussetzungen


Subjects to be covered include: Lie groups and algebras, the exponential map, the Peter-Weyl theorem, maximal tori, roots and weights, the Weyl group, the Weyl character formula and representations of the classical groups. In addition, some applications to physics may be discussed.


After successful completion of this module, students will have a basic understanding of the representation theory of compact groups. Key learning goals include a thorough grasp of the relationship between a Lie group and its Lie algebra, and the ability to explain the resulting consequences for representation theory. Students know how to analyze Lie groups and their representations from algebraic, differential geometric and analytical viewpoints. This involves, in particular, the application of methods for constructing and decomposing representations.


MA1001 - Analysis 1
MA1002 - Analysis 2
MA1101 - Linear Algebra and Discrete Structures1
MA1002 - Linear Algebra and Discrete Structures 2

Lehrveranstaltungen, Lern- und Lehrmethoden und Literaturhinweise

Lehrveranstaltungen und Termine

VO 2 Representations of Compact Groups König, R. Fr, 10:15–11:45, 5610.02.011
UE 2 Representations of Compact Groups (Exercise Session) König, R. Fr, 08:30–10:00, 5610.02.011

Lern- und Lehrmethoden

Lectures, Exercises, Homework
This module consists of lectures together with accompanying practice sessions. The lectures will convey relevant concepts, mathematical results and proof methods along with concrete examples by means of board work and through discussion with the students. This is intended to motivate students to study the literature and approach problems independently. Practice sessions will be offered which complement the theoretical material developed in the lectures. Exercise sheets and solutions will be provided, which will help students to deepen their understanding, and independently assess their progress. The practice sessions will be guided initially, but will proceed throughout the term to more independent work by students individually as well as in small groups.


Board work, Exercise sheets


Primarily: Barry Simon, Representations of Finite and Compact Groups, AMS 1996.


Beschreibung der Prüfungs- und Studienleistungen

The module examination is based on an oral exam (20 minutes).
The exam will assess the ability to give precise definitions, prove selected theorems involving algebraic, differential geometric and analytical arguments, and apply results and techniques to analyze, classify and construct various algebraic objects appearing in the study of Lie groups and algebras. This includes, in particular, the problem of decomposing representations into irreducibles. With suitably chosen examples, the ability to transfer results and techniques to the analysis of related problems involving representation-theoretic concepts will be tested.


Eine Wiederholungsmöglichkeit wird am Semesterende angeboten.

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