Specht module

Summary

For each partition $\lambda$ of $n$, the Specht module $S^\lambda$ is a representation of the symmetric group $S_n$ built from Young tableaux of shape $\lambda$. Over a field of characteristic $0$, the Specht modules are irreducible and give every irreducible representation of $S_n$ exactly once. They are defined over any field, even over the integers. The dimension of $S^\lambda$ is the number of standard Young tableaux of shape $\lambda$, given by the hook length formula.