Smooth representations of GL_m(D) VI : semisimple types

2010/09/06 by Vincent Sécherre, Sécherre, Vincent, Shaun Stevens +1 · 1 citation
Mathematics · #22E50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1009.1062

openalex publication_date 2010/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We give a complete description of the category of smooth complex representations of the multiplicative group of a central simple algebra over a locally compact nonarchimedean local field. More precisely, for each inertial class in the Bernstein spectrum, we construct a type and compute its Hecke algebra. The Hecke algebras that arise are all naturally isomorphic to products of affine Hecke algebras of type A. We also prove that, for cuspidal classes, the simple type is unique up to conjugacy.

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