Smooth Representations of GLm(D) VI: Semisimple Types

Secherre, V and Stevens, S (2012) Smooth Representations of GLm(D) VI: Semisimple Types. International Mathematics Research Notices, 2012 (13). pp. 2994-3039. ISSN 1073-7928

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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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
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Date Deposited: 20 Oct 2011 10:31
Last Modified: 24 Jul 2019 13:46
URI: https://ueaeprints.uea.ac.uk/id/eprint/35101
DOI: 10.1093/imrn/rnr122

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