Elements of Representation Theory

Abstract

The final chapter of the book presents the basic elements of representation theory, especially finite-dimensional representations of finite groups. For instance, it is proved that every representation of a finite group is a direct sum of irreducible representations, and that a finite group has only a finite number of distinct (up to equivalence) irreducible representations. At the end of the chapter, irreducible representations (characters) of abelian finite groups are considered.