First we will briefly review the representation theory of finite groups. The goal of the talk will then be to work out this theory explicitly for the symmetric group S_n. We will use Young tableaux to construct the irreducible representations of S_n, called Specht modules.
We then construct the graded ring of representations R and give an isomorphism between R and the graded ring of symmetric functions. Using this isomorphism, we can transfer what we know about symmetric functions to deduce corresponding facts about representations.