Combinatória das representações irredutíveis do grupo simétrico

Abstract

In this work, we present the basic representation theory of the symmetric group and its combinatorial aspects. The main objective of this work is to construct a complete set of irreducible and inequivalent representations of the symmetric group, in terms of its partition and combinatorial concepts related to Young’s tableau. We will see that this combinatorial object will provide us two ways of describing the irreducible representations of the symmetric group, a politabloid pathway, and an alternative via idempotent group algebra, and that, in fact, these two approaches are isomorphic. We will cover some interesting results, such as the Young’s rule, the branching rule, and the Robinson-Schensted’s combinatorial matching algorithm.