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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.13018 |
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Table of 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 $G^Γ$.