On eigenvalues of permutations in irreducible representations of symmetric and alternating groups

Alexey Staroletov

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arXiv · 2501.17571

On eigenvalues of permutations in irreducible representations of symmetric and alternating groups

Alexey Staroletov

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Abstract

Denote the symmetric group of degree $n$ by $S_n$. Let $\rho$ be an irreducible representation of $S_n$ over the field of complex numbers and $\sigma\in S_n$. In this paper, we describe the set of eigenvalues of $\rho(\sigma)$. Based on this result, we also obtain a description in the case of alternating groups.

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Alexey Staroletov. 2025-01-29. On eigenvalues of permutations in irreducible representations of symmetric and alternating groups. https://arxiv.org/abs/2501.17571

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