The $p$-rationality of height-zero characters
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913600827817984 |
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| author | Hung, Nguyen N. Fry, A. A. Schaeffer |
| author_facet | Hung, Nguyen N. Fry, A. A. Schaeffer |
| contents | We propose and present evidence for a conjectural global-local phenomenon concerning the $p$-rationality of $p$-height-zero characters. Specifically, if $χ$ is a height-zero character of a finite group $G$ and $D$ is a defect group of the $p$-block of $G$ containing $χ$, then the $p$-rationality of $χ$ can be captured inside the normalizer $N_G(D)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $p$-rationality of height-zero characters Hung, Nguyen N. Fry, A. A. Schaeffer Group Theory Representation Theory We propose and present evidence for a conjectural global-local phenomenon concerning the $p$-rationality of $p$-height-zero characters. Specifically, if $χ$ is a height-zero character of a finite group $G$ and $D$ is a defect group of the $p$-block of $G$ containing $χ$, then the $p$-rationality of $χ$ can be captured inside the normalizer $N_G(D)$. |
| title | The $p$-rationality of height-zero characters |
| topic | Group Theory Representation Theory |
| url | https://arxiv.org/abs/2412.05703 |