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arXiv · 1110.2701

Repr\'esentations banales de GL(m,D)

Alberto Minguez·Vincent Sécherre
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Abstract

Soit F un corps commutatif localement compact non archim\'edien de caract\'eristique r\'esiduelle p, soit D une F-alg\`ebre \`a division centrale de dimension finie et soit R un corps alg\'ebriquement clos de caract\'eristique diff\'erente de p. Nous d\'efinissons la notion de R-repr\'esentation irr\'eductible banale de G=GL(m,D), notion qui g\'en\'eralise celle de caract\'eristique banale pour G, et qui repose sur une condition portant sur le support cuspidal de la repr\'esentation et d\'ependant de la caract\'eristique de R. Lorsque le corps R est de caract\'eristique banale, en particulier lorsque R est le corps des nombres complexes, toute R-repr\'esentation irr\'eductible de G est banale. Nous donnons dans cet article une classification des R-repr\'esentations irr\'eductibles banales de G en termes de multisegments dits banals. Lorsque R est le corps des nombres complexes, notre m\'ethode fournit une nouvelle preuve, enti\`erement locale, de la classification de Tadic des repr\'esentations lisses irr\'eductibles complexes de G.

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BibTeXRIS

Alberto Minguez, Vincent Sécherre. 2011-10-12. Repr\'esentations banales de GL(m,D). https://doi.org/10.1112/s0010437x12000590

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