Restricting admissible representations to fixed-point subgroups

Peter Latham; Monica Nevins

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arXiv · 2104.01510

Restricting admissible representations to fixed-point subgroups

Peter Latham·Monica Nevins

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Abstract

Given a $p$-adic group $G$ equipped with an action of a finite group $\Gamma\subset\mathrm{Aut}_F(\mathbf{G})$, and a reductive fixed-point subgroup $G^\Gamma$, we establish a relationship between constructions of types for these two groups due to Yu, Kim--Yu and Fintzen, and generalizes the relationship between general linear and classical groups observed by Stevens. As an application, given a parabolically induced or supercuspidal representation $\pi$ of $G$, we explicitly identify a number of the inertial equivalence classes occurring in the representation $\pi|_{G^{[\Gamma]}}$.

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BibTeX RIS

Peter Latham, Monica Nevins. 2021-04-04. Restricting admissible representations to fixed-point subgroups. https://arxiv.org/abs/2104.01510

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