On the maximal dimension of an irreducible representation of the symmetric group

Amol Aggarwal, Dor Elboim

We prove that the maximal dimension $d_N$ of an irreducible representation of the symmetric group $S_N$ satisfies $$d_N=\sqrt{N!} \, e^{-(\mathfrak{d}+o(1))\sqrt{N} }, \quad N\to \…