Representations of Finite Groups

Abstract

The most effective tools in applying group theoretical methods to physical problems are the representations of the groups in “physical” spaces and the characters of these representations. Of all the possible representations, those by linear operators, or more specifically, by matrices, are the most essential ones. The basic spaces are the linear (vector) spaces, which are discussed first in this chapter. Then the properties of different representations are outlined with special emphasis on the irreducible ones. Finally we investigate product representations of groups.