On eigenvalues of permutations in irreducible representations of symmetric and alternating groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911188207534080 |
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| author | Staroletov, Alexey |
| author_facet | Staroletov, Alexey |
| contents | Denote the symmetric group of degree $n$ by $S_n$. Let $ρ$ be an irreducible representation of $S_n$ over the field of complex numbers and $σ\in S_n$. In this paper, we describe the set of eigenvalues of $ρ(σ)$. Based on this result, we also obtain a description in the case of alternating groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On eigenvalues of permutations in irreducible representations of symmetric and alternating groups Staroletov, Alexey Group Theory Representation Theory 20C30, 20C15, 05E10 Denote the symmetric group of degree $n$ by $S_n$. Let $ρ$ be an irreducible representation of $S_n$ over the field of complex numbers and $σ\in S_n$. In this paper, we describe the set of eigenvalues of $ρ(σ)$. Based on this result, we also obtain a description in the case of alternating groups. |
| title | On eigenvalues of permutations in irreducible representations of symmetric and alternating groups |
| topic | Group Theory Representation Theory 20C30, 20C15, 05E10 |
| url | https://arxiv.org/abs/2501.17571 |