Representation Theory of Finite and Compact Groups

Code: MA626 | L-T-P-C: 3-0-0-6

Prerequisites: MA 224 or MA 541 or equivalent

Representations of finite groups, sub-representations, characters of a representation, irreducible representations and Schur's lemma. Topological group, Haar measures, existence theorem for Haar measure on a locally compact group, left and right regular representations, Induced representations. Representations of compact groups, unitary irreducible representations, Peter-Weyl theorems, representations of SO(2), SU(2) etc., Fourier series on the unit sphere S^(n-1).

Texts/References:

1. J. P. Serre, Linear Representations of Finite groups, Springer-Verlag, 1977.
2. Barry Simon, Representation of Finite and Compact Groups, AMS, 1996.
3. G. B. Folland, A course in abstract Harmonic analysis, CRC Press, Boca Raton, 1995