Integrated MSc-PhD Program

SYLLABUS

KSM3E06: Representation theory

Generalities on linear representations, Subrepresentations, Irreducible representations, Tensor product of two representations, Symmetric square and alternating square, The character of a representation, Schur’s lemma; basic applications, Orthogonality relations for characters, Decomposition of the regular representation, Number of irreducible representations, Canonical decomposition of a representation, Explicit decomposition of a representation, Subgroups, products, induced representations, Abelian subgroups, Product of two groups, Induced representations.

Suggested texts:

1. 1. 1. 1. 1. 1. Representation Theory, A First Course – Fulton and Harris
               2. Linear Representations of Finite Groups – Jean-Pierre Serre