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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.08265 |
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| _version_ | 1866929589264056320 |
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| author | Larsen, Michael |
| author_facet | Larsen, Michael |
| contents | Let $S_n$ denote a symmetric group, $χ$ an irreducible character of $S_n$, and $g\in S_n$ an element which decomposes into $k$ disjoint cycles, where $1$-cycles are included. Then $|χ(g)|\le k!$, and this upper bound is sharp for fixed $k$ and varying $n$, $χ$, and $g$. This implies a sharp upper bound of $k!$ for unipotent character values of $SL_n(q)$ at regular semisimple elements with characteristic polynomial $P(t)=P_1(t)\cdots P_k(t)$, where the $P_i$ are irreducible over $F_q[t]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp character bounds for symmetric groups in terms of partition length Larsen, Michael Representation Theory Let $S_n$ denote a symmetric group, $χ$ an irreducible character of $S_n$, and $g\in S_n$ an element which decomposes into $k$ disjoint cycles, where $1$-cycles are included. Then $|χ(g)|\le k!$, and this upper bound is sharp for fixed $k$ and varying $n$, $χ$, and $g$. This implies a sharp upper bound of $k!$ for unipotent character values of $SL_n(q)$ at regular semisimple elements with characteristic polynomial $P(t)=P_1(t)\cdots P_k(t)$, where the $P_i$ are irreducible over $F_q[t]$. |
| title | Sharp character bounds for symmetric groups in terms of partition length |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2411.08265 |