Degrees and prime power order zeros of characters of symmetric and alternating groups
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911269282381824 |
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| author | Giannelli, Eugenio Law, Stacey McDowell, Eoghan |
| author_facet | Giannelli, Eugenio Law, Stacey McDowell, Eoghan |
| contents | We show that the $p$-part of the degree of an irreducible character of a symmetric group is completely determined by the set of vanishing elements of $p$-power order. As a corollary we deduce that the set of zeros of prime power order controls the degree of such a character. The same problem is analysed for alternating groups, where we show that when $p=2$ this data can only be determined up to two possibilities. We prove analogous statements for the defect of the $p$-block containing the character and for the $p$-height of the character. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02686 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degrees and prime power order zeros of characters of symmetric and alternating groups Giannelli, Eugenio Law, Stacey McDowell, Eoghan Representation Theory Group Theory 20C30 (primary) 20C15 (secondary) We show that the $p$-part of the degree of an irreducible character of a symmetric group is completely determined by the set of vanishing elements of $p$-power order. As a corollary we deduce that the set of zeros of prime power order controls the degree of such a character. The same problem is analysed for alternating groups, where we show that when $p=2$ this data can only be determined up to two possibilities. We prove analogous statements for the defect of the $p$-block containing the character and for the $p$-height of the character. |
| title | Degrees and prime power order zeros of characters of symmetric and alternating groups |
| topic | Representation Theory Group Theory 20C30 (primary) 20C15 (secondary) |
| url | https://arxiv.org/abs/2504.02686 |