Representations of the Symmetric Group

Abstract

The symmetric (permutation) group is an important prototype of finite groups. In fact, Cayley’s theorem (see Rotman in An Introduction to the Theory of Groups, Allyn and Bacon, Needham Heights, [Rotm 84, p. 46] for a proof) states that any finite group of order n is isomorphic to a subgroup of Sn. Moreover, the representation of Snleads directly to the representation of many of the Lie groups encountered in physical applications. It is, therefore worthwhile to devote some time to the analysis of the representations of Sn.