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SoSe 15: Representation theory of finite groups

Rostislav Devyatov

Hinweise für Studierende

Die Themen werden am 13.04.2015 ausgeteilt.
Students will be able to give talks in English or German, whatever they prefer.

Zusätzl. Angaben / Voraussetzungen

Lineare Algebra I

Kommentar

Historically, finite groups appeared in mathematics together with an action on some object, for example, as the groups of symmetries of polygons or polytopes. We are going to study, in some sense, the easiest possible actions of finite groups, namely, the linear actions on vector spaces. Such actions are called representations of finite groups. We will only consider representations in complex vector spaces.

Preliminary program:

1. Basic definitions and operations: direct sum, tensor product, dual.
2. Examples: some particular groups of small order, abelian groups (without proof of the completeness of the list so far).
3. Irreducible representations, complete reducibility theorem, proof using projections.
4. Unitary representations, second proof of complete reducibility theorem.
5. Functions on the group, orthogonality properties of matrix elements of representation, characters.
6. Applications of character theory.
7. Divisibility properties of dimensions.
8. Representation theory of symmetric groups.
9. Induced representations.
10. A criterium for irreducibility of an induced representation. Schließen

Literaturhinweise

J.-P. Serre, Linear Representations of Finite Groups, GTM 42
W. Fulton, J. Harris, Representation Theory - A First Course, GTM 129

13 Termine

Regelmäßige Termine der Lehrveranstaltung

Mo, 12:00 - 14:00 13 Termine

Mo, 13.04.2015 12:00 - 14:00

Dozenten:
Rostislav Devyatov