Young's Natural Representations of ${\mathcal{S}}_4$

Abstract

We calculate all inequivalent irreducible representations of ${\S }_4$ by specifying the matrices for adjacent transpositions and indicating how to obtain general permutations in ${\S }_4$ from these transpositions. We employ standard Young tableaux methods as found in Sagan's \emph{The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions} (2001).