Axiomatic representation theory for finite groups

Representation Theory for Finite Groups

We cover some of the foundational results of representation theory including Maschke’s Theorem, Schur’s Lemma, and the Schur Orthogonality Relations. We consider character theory, constructions of representations, and conjugacy classes. Finally, we touch upon Pontryagin Duality for abelian groups and Young Tableaux for the Symmetric Group.

Representation Theory of Finite Groups

1.1. Let G be a finite group. We write the multiplication in G using either concatenation or · (so gg′ = g · g′) and we will denote the unit in G by 1. Throughout these notes, C denotes any algebraically closed field of characteristic 0. Of course, it’s fine to have the complex numbers in mind, but there’s no problem with using Q or anything else. In particular, the use of analytic properties o...

Representation Theory of Finite Groups

Representation Theory of Finite Groups

Preface This book arose out of course notes for a fourth year undergraduate/first year graduate course that I taught at Carleton University. The goal was to present group representation theory at a level that is accessible to students who have not yet studied module theory and who are unfamiliar with tensor products. For this reason, the Wedderburn theory of semisimple algebras is completely av...

Introduction to representation theory of finite groups