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On the maximal dimension of an irreducible representation of the symmetric group
Amol Aggarwal, Dor Elboim · 2026-05-26 · via math updates on arXiv.org

We prove that the maximal dimension $d_N$ of an irreducible representation of the symmetric group $S_N$ satisfies $$d_N=\sqrt{N!} \, e^{-(\mathfrak{d}+o(1))\sqrt{N} }, \quad N\to \infty,$$ for some constant $\mathfrak{d}>0$. This answers a question raised by Vershik--Kerov in 1985.

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