Vol. 312, No. 1, 2021

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Restricting supercuspidal representations via a restriction of data

Vol. 312 (2021), No. 1, 1–39
Abstract

Let $F$ be a nonarchimedean local field of residual characteristic $p$. Let $\mathbb{𝔾}$ be a connected reductive group defined over $F$ which splits over a tamely ramified extension, and set $G=\mathbb{𝔾}\left(F\right)$. We assume that $p$ does not divide the order of the Weyl group of $\mathbb{𝔾}$. Given a closed connected $F$-subgroup $ℍ$ that contains the derived subgroup of $\mathbb{𝔾}$, we study the restriction to $H=ℍ\left(F\right)$ of an irreducible supercuspidal representation $\pi ={\pi }_{G}\left(\Psi \right)$ of $G$, where $\Psi$ is a $G$-datum as per the J.-K. Yu construction. We provide a full description of $\pi {|}_{H}$ into irreducible components, with multiplicity, via a restriction of data which constructs $H$-data from $\Psi$. Analogously, we define a restriction of Kim–Yu types to study the restriction of irreducible representations of $G$ which are not supercuspidal.

Keywords
supercuspidal representations, p-adic group, restriction, multiplicity
Primary: 22E50