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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.13152 |
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| _version_ | 1866909995227938816 |
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| author | Gustavsson, Bim |
| author_facet | Gustavsson, Bim |
| contents | Let $p$ be an odd prime. We show that for sufficiently large $n$, every $2$-block of $\mathfrak{S}_n$ and $\mathfrak{A}_n$ contains an ordinary irreducible character of degree divisible by $p$. For almost all $2$-blocks of $\mathfrak{A}_n$, we classify whether it contains a rational valued ordinary irreducible character of degree divisible by $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13152 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Character degrees in $2$-blocks of $\mathfrak{S}_n$ and $\mathfrak{A}_n$ Gustavsson, Bim Representation Theory Let $p$ be an odd prime. We show that for sufficiently large $n$, every $2$-block of $\mathfrak{S}_n$ and $\mathfrak{A}_n$ contains an ordinary irreducible character of degree divisible by $p$. For almost all $2$-blocks of $\mathfrak{A}_n$, we classify whether it contains a rational valued ordinary irreducible character of degree divisible by $p$. |
| title | Character degrees in $2$-blocks of $\mathfrak{S}_n$ and $\mathfrak{A}_n$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.13152 |