Smooth representations of GL_m(D) VI : semisimple types

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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Submitted on : Wednesday, February 22, 2012 - 11:29:52 AM
Last modification on : Wednesday, January 23, 2019 - 2:39:26 PM

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  • HAL Id : hal-00672889, version 1
  • ARXIV : 1009.1062

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Vincent Sécherre, Shaun Stevens. Smooth representations of GL_m(D) VI : semisimple types. 2010. ⟨hal-00672889⟩

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