19221910
Seminar
SoSe 15: Representation theory of finite groups
Rostislav Devyatov
Information for students
Die Themen werden am 13.04.2015 ausgeteilt.
Students will be able to give talks in English or German, whatever they prefer.
Students will be able to give talks in English or German, whatever they prefer.
Additional information / Pre-requisites
Lineare Algebra I
Comments
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.
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. close
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. close
Suggested reading
J.-P. Serre, Linear Representations of Finite Groups, GTM 42
W. Fulton, J. Harris, Representation Theory - A First Course, GTM 129
W. Fulton, J. Harris, Representation Theory - A First Course, GTM 129
13 Class schedule
Regular appointments
Mon, 2015-04-13 12:00 - 14:00
Mon, 2015-04-20 12:00 - 14:00
Mon, 2015-04-27 12:00 - 14:00
Mon, 2015-05-04 12:00 - 14:00
Mon, 2015-05-11 12:00 - 14:00
Mon, 2015-05-18 12:00 - 14:00
Mon, 2015-06-01 12:00 - 14:00
Mon, 2015-06-08 12:00 - 14:00
Mon, 2015-06-15 12:00 - 14:00
Mon, 2015-06-22 12:00 - 14:00
Mon, 2015-06-29 12:00 - 14:00
Mon, 2015-07-06 12:00 - 14:00
Mon, 2015-07-13 12:00 - 14:00