A nonabelian Fourier transform for tempered unipotent representations

2021/06/26 by Anne‐Marie Aubert, Aubert, Anne-Marie, Dan Ciubotaru +3
Mathematics · #20C33 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2106.13969

openalex publication_date 2021/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define an involution on the space of compact tempered unipotent representations of inner twists of a split simple p-adic group G and investigate its behaviour with respect to restrictions to reductive quotients of maximal compact open subgroups. In particular, we formulate a precise conjecture about the relation with a version of Lusztig's nonabelian Fourier transform on the space of unipotent representations of the (possibly disconnected) reductive quotients of maximal compact subgroups. We give evidence of the conjecture, including proofs for SL_n and PGL_n.

Citations

• Affine Hecke algebras for Langlands parameters

Related

• The nonabelian Fourier transform for elliptic unipotent representations of exceptional p-adic groups
• On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups
• Théorème de Paley-Wiener pour les fonctions de Whittaker sur un groupe réductif p-adique
• Unipotent almost characters of simple p-adic groups, II
• Fourier Transform and the minimal representation of E₇