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Publication Date:
January 2009
ISSN:
1435-5345
DOI:
10.1515/CRELLE.2009.007

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Journal für die reine und angewandte Mathematik

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Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Proof of the Tadić conjecture (U0) on the unitary dual of GLm(D)

Vincent Sécherre1

1Institut de Mathématiques de Luminy, CNRS UMR 6206, Université de la Méditerranée, 163 avenue de Luminy, 13288 Marseille Cedex 9, France. e-mail: secherre@iml.univ-mrs.fr

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2009, Issue 626, Pages 187–203, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2009.007, January 2009

Publication History:
Received:
2007-05-24
Revised:
2007-10-11
Published Online:
2009-01-08

Abstract

Let F be a non-Archimedean local field of characteristic 0, and let D be a finite-dimensional central division algebra over F. We prove that any unitary irreducible smooth representation of a Levi subgroup of GLm(D), with m ≧ 1, induces irreducibly to GLm(D). This ends the classification of the unitary dual of GLm(D) initiated by Tadić.

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