Duke Mathematical Journal

Un renforcement de la propriété (T)

Vincent Lafforgue

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Résumé

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.

Abstract

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

Article information

Source
Duke Math. J., Volume 143, Number 3 (2008), 559-602.

Dates
First available in Project Euclid: 3 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1212500467

Digital Object Identifier
doi:10.1215/00127094-2008-029

Mathematical Reviews number (MathSciNet)
MR2423763

Zentralblatt MATH identifier
1158.46049

Subjects
Primary: 46B04: Isometric theory of Banach spaces 20F67: Hyperbolic groups and nonpositively curved groups
Secondary: 20E08: Groups acting on trees [See also 20F65]

Citation

Lafforgue, Vincent. Un renforcement de la propriété (T). Duke Math. J. 143 (2008), no. 3, 559--602. doi:10.1215/00127094-2008-029. https://projecteuclid.org/euclid.dmj/1212500467


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