Fusion invariant characters of p-groups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910561302740992 |
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| author | Sambale, Benjamin |
| author_facet | Sambale, Benjamin |
| contents | We consider complex characters of a p-group P, which are invariant under a fusion system F on P. Extending a theorem of Bárcenas--Cantarero to non-saturated fusion systems, we show that the number of indecomposable F-invariant characters of P is greater or equal than the number of F-conjugacy classes of P. We further prove that these two quantities coincide whenever F is realized by a p-solvable group. On the other hand, we observe that this is false for constrained fusion systems in general. Finally, we construct a saturated fusion system with an indecomposable F-invariant character, which is not a summand of the regular character of P. This disproves a recent conjecture of Cantarero--Combariza. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fusion invariant characters of p-groups Sambale, Benjamin Representation Theory Group Theory We consider complex characters of a p-group P, which are invariant under a fusion system F on P. Extending a theorem of Bárcenas--Cantarero to non-saturated fusion systems, we show that the number of indecomposable F-invariant characters of P is greater or equal than the number of F-conjugacy classes of P. We further prove that these two quantities coincide whenever F is realized by a p-solvable group. On the other hand, we observe that this is false for constrained fusion systems in general. Finally, we construct a saturated fusion system with an indecomposable F-invariant character, which is not a summand of the regular character of P. This disproves a recent conjecture of Cantarero--Combariza. |
| title | Fusion invariant characters of p-groups |
| topic | Representation Theory Group Theory |
| url | https://arxiv.org/abs/2401.15706 |