HSE
Math in Moscow
Math in Moscow schedule

Vladlen Timorin

Basic Representation Theory

The final exam will take place on Tuesday, December, at 6:00pm! Practice problems are posted here . Since the final exam covers all topics discussed since September, you may also find the practice problems for the midterm ( here ) helpful.

Course Outline

Introduction. Basic concepts of Representation Theory.
Invariant subspaces and complete reducibility.
Basic operations on representations.
Properties of complex irreducible representations.
The character theory.
Representations of SU(2) and SO(3).
Lie group and Lie algebras.

References:

Vinberg, Ernest B., Linear Representations of Groups, Birkhauser Basel, 1989
Fulton, William; Harris, Joe., Representation theory. A first course, Graduate Texts in Mathematics, Readings in Mathematics, 129, New York: Springer-Verlag, 1991.
Sheinman, Oleg K., Basic Representation Theory, Moscow: MCCME, 2007.
Serre, Jean-Pierre, Linear Representations of Finite Groups, Springer-Verlag, 1977.
Vinberg, Ernest B., A Course in Algebra, Graduate Studies in Mathematics, 56, AMS, 2003.