Lifting semisimple characters of $p$-adic types from fixed-point subgroups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917273820725248 |
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| author | Bourgeois, Adèle Nevins, Monica |
| author_facet | Bourgeois, Adèle Nevins, Monica |
| contents | Given a $p$-adic group $G=\mathbf{G}(F)$ and a finite group $Γ\subset\mathrm{Aut}_F(\mathbf{G})$ such that the fixed-point subgroup $\mathbf{G}^Γ$ is reductive, we show that every semisimple character (in the sense of Bushnell and Kutzko) of a type for $G^Γ= \mathbf{G}^Γ(F)$ arises as the restriction of a semisimple character of a type for $G$. We achieve this by explicitly lifting the truncated Kim--Yu datum (or character-datum) that parametrizes the semisimple character for $G^Γ$ to a character-datum that parametrizes a semisimple character for $G$. Our proof, which is of independent interest, uses state-of-the-art techniques and, as a special case, defines a lift of a Howe factorization of a character of a maximal torus of $G^Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13018 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lifting semisimple characters of $p$-adic types from fixed-point subgroups Bourgeois, Adèle Nevins, Monica Representation Theory 22E50 Given a $p$-adic group $G=\mathbf{G}(F)$ and a finite group $Γ\subset\mathrm{Aut}_F(\mathbf{G})$ such that the fixed-point subgroup $\mathbf{G}^Γ$ is reductive, we show that every semisimple character (in the sense of Bushnell and Kutzko) of a type for $G^Γ= \mathbf{G}^Γ(F)$ arises as the restriction of a semisimple character of a type for $G$. We achieve this by explicitly lifting the truncated Kim--Yu datum (or character-datum) that parametrizes the semisimple character for $G^Γ$ to a character-datum that parametrizes a semisimple character for $G$. Our proof, which is of independent interest, uses state-of-the-art techniques and, as a special case, defines a lift of a Howe factorization of a character of a maximal torus of $G^Γ$. |
| title | Lifting semisimple characters of $p$-adic types from fixed-point subgroups |
| topic | Representation Theory 22E50 |
| url | https://arxiv.org/abs/2602.13018 |