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15 June 2008 Un renforcement de la propriété (T)
Vincent Lafforgue
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Duke Math. J. 143(3): 559-602 (15 June 2008). DOI: 10.1215/00127094-2008-029

Abstract

On montre que certains groupes de Lie réels ou p-adiques vérifient une propriété (T) renforcée, pour des actions à petite croissance exponentielle dans des espaces de Hilbert ou des espaces de Banach uniformément convexes. On montre que les groupes hyperboliques n'ont pas cette propriété. On construit des familles d'expanseurs ne se plongeant uniformement dans aucun espace de Banach uniformement convexe.

We show a strong form of property (T) for some real or p-adic semisimple groups. This strong form of property (T) means that the trivial representation is isolated among representations with a small exponential growth in Hilbert spaces or even in uniformly convex Banach spaces.

We show that hyperbolic groups do not have strong property (T). We construct families of expanders which do not imbed uniformly in any uniformly convex Banach space

Citation

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Vincent Lafforgue. "Un renforcement de la propriété (T)." Duke Math. J. 143 (3) 559 - 602, 15 June 2008. https://doi.org/10.1215/00127094-2008-029

Information

Published: 15 June 2008
First available in Project Euclid: 3 June 2008

zbMATH: 1158.46049
MathSciNet: MR2423763
Digital Object Identifier: 10.1215/00127094-2008-029

Subjects:
Primary: 20F67 , 46B04
Secondary: 20E08

Rights: Copyright © 2008 Duke University Press

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Vol.143 • No. 3 • 15 June 2008
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