Vol. 312, No. 1, 2021

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Restricting supercuspidal representations via a restriction of data

Adèle Bourgeois

Vol. 312 (2021), No. 1, 1–39
Abstract

Let F be a nonarchimedean local field of residual characteristic p. Let 𝔾 be a connected reductive group defined over F which splits over a tamely ramified extension, and set G = 𝔾(F). We assume that p does not divide the order of the Weyl group of 𝔾. Given a closed connected F-subgroup that contains the derived subgroup of 𝔾, we study the restriction to H = (F) of an irreducible supercuspidal representation π = πG(Ψ) of G, where Ψ is a G-datum as per the J.-K. Yu construction. We provide a full description of π|H into irreducible components, with multiplicity, via a restriction of data which constructs H-data from Ψ. 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
Mathematical Subject Classification
Primary: 22E50
Milestones
Received: 14 September 2020
Revised: 17 March 2021
Accepted: 23 March 2021
Published: 4 August 2021
Authors
Adèle Bourgeois
Department of Mathematics and Statistics
University of Ottawa
Ottawa, ON
Canada