C^∗-blocks and crossed products for classical p-adic groups

2020/02/28 by Alexandre Afgoustidis, Anne‐Marie Aubert, Afgoustidis, Alexandre +1
Mathematics · #22D25 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2002.12864

openalex publication_date 2020/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a real or p-adic reductive group. We consider the tempered dual of G, and its connected components. For real groups, Wassermann proved in 1987, by noncommutative-geometric methods, that each connected component has a simple geometric structure which encodes the reducibility of induced representations. For p-adic groups, each connected component of the tempered dual comes with a compact torus equipped with a finite group action, and we prove that a version of Wassermann's theorem holds true under a certain geometric assumption on the structure of stabilizers for that action. We then focus on the case where G is a quasi-split symplectic, orthogonal or unitary group, and explicitly determine the connected components for which the geometric assumption is satisfied.

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