Minimal numbers of linear constituents in Sylow restrictions for symmetric groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915301330780160 |
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| author | Gustavsson, Bim Law, Stacey |
| author_facet | Gustavsson, Bim Law, Stacey |
| contents | Let $p$ be any prime. We determine precisely those irreducible characters of symmetric groups which contain at most $p$ distinct linear constituents in their restriction to a Sylow $p$-subgroup, answering a question of Giannelli and Navarro. Moreover, we identify all of the linear constituents of such characters, and in the case $p = 2$ explicitly calculate a new class of Sylow branching coefficients for symmetric groups indexed by so-called almost hook partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17904 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal numbers of linear constituents in Sylow restrictions for symmetric groups Gustavsson, Bim Law, Stacey Representation Theory Combinatorics Let $p$ be any prime. We determine precisely those irreducible characters of symmetric groups which contain at most $p$ distinct linear constituents in their restriction to a Sylow $p$-subgroup, answering a question of Giannelli and Navarro. Moreover, we identify all of the linear constituents of such characters, and in the case $p = 2$ explicitly calculate a new class of Sylow branching coefficients for symmetric groups indexed by so-called almost hook partitions. |
| title | Minimal numbers of linear constituents in Sylow restrictions for symmetric groups |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2505.17904 |