Irreducible Representations of  \(S_n\)

The aim of this report is to describe all of the irreducible representations of the symmetric group \(S_n\). Each conjugacy class of Sn has an associated partition \(\lambda\), and we will use this partition to construct an irreducible representation \(V_\lambda\). Because of this correspondence between conjugacy classes and irreducible representations, we know that these \(V_\lambda\) form the complete set of irreducible representations of \(S_n\). Furthermore, we shall state Frobenius’s formula - a way to compute the character of \(V_\lambda\). We then use this to find a nice algorithm for computing the dimension of \(V_\lambda\).