On the irreducible representation of symmetric groups S6 and S7

Abstract

The focus here is on the representation theory of the symmetric group over a field of char acteristic zero. Every representation is built out of irreducible representations. The main aim of this dissertation is to describe these irreducible representations for the symmetric group using a combinatorial approach. Construct the Specht modules and use them to characterize the irreducible representations of the symmetric groups S6 and S7. In order to define the Specht modules there’s need to introduce Young diagrams, Young tableaux, tabloids and polytabloids and show that the polytabloids associated with the standard Young tableaux form a basis for the Specht modules. Then show that the Specht modules over C are exactly all of the irreducible representations over C. The dimensions of the irreducible representations is calculated using Hook’s length formula.