Representation Theory of the Symmetric Group

Abstract

No group is of greater importance than the symmetric group. After all, any group can be embedded as a subgroup of a symmetric group. In this chapter, we construct the irreducible representations of the symmetric group S n . The character theory of the symmetric group is a rich and important theory filled with important connections to combinatorics. One can find whole books dedicated to this subject, cf. [16, 17, 19, 12]. Moreover, there are important applications to such diverse areas as voting and card shuffling [7, 8, 3].