On a variant of Kazhdan's property (T) for subgroups of semisimple groups

Mohammed Bachir Bekka; Nicolas Louvet

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 4, page 1065-1078
  • ISSN: 0373-0956

Abstract

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Let Γ be an irreducible lattice in a product G of simple groups. Assume that G has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of Γ in terms of the topology of the dual space G ^ of G .We use this result to give a new proof for the triviality of the first cohomology group of Γ with coefficients in a finite dimensional unitary representation.

How to cite

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Bekka, Mohammed Bachir, and Louvet, Nicolas. "On a variant of Kazhdan's property (T) for subgroups of semisimple groups." Annales de l'institut Fourier 47.4 (1997): 1065-1078. <http://eudml.org/doc/75254>.

@article{Bekka1997,
abstract = {Let $\Gamma $ be an irreducible lattice in a product $G$ of simple groups. Assume that $G$ has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of $\Gamma $ in terms of the topology of the dual space $\widehat\{G\}$ of $G$.We use this result to give a new proof for the triviality of the first cohomology group of $\Gamma $ with coefficients in a finite dimensional unitary representation.},
author = {Bekka, Mohammed Bachir, Louvet, Nicolas},
journal = {Annales de l'institut Fourier},
keywords = {discrete subgroups of Lie groups; Kazhdan's property; cohomology; unitary representation},
language = {eng},
number = {4},
pages = {1065-1078},
publisher = {Association des Annales de l'Institut Fourier},
title = {On a variant of Kazhdan's property (T) for subgroups of semisimple groups},
url = {http://eudml.org/doc/75254},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Bekka, Mohammed Bachir
AU - Louvet, Nicolas
TI - On a variant of Kazhdan's property (T) for subgroups of semisimple groups
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 4
SP - 1065
EP - 1078
AB - Let $\Gamma $ be an irreducible lattice in a product $G$ of simple groups. Assume that $G$ has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of $\Gamma $ in terms of the topology of the dual space $\widehat{G}$ of $G$.We use this result to give a new proof for the triviality of the first cohomology group of $\Gamma $ with coefficients in a finite dimensional unitary representation.
LA - eng
KW - discrete subgroups of Lie groups; Kazhdan's property; cohomology; unitary representation
UR - http://eudml.org/doc/75254
ER -

References

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  10. [Hum] J.E. HUMPHREYS, Arithmetic groups, Lecture Notes in Math., 789, Springer, 1980. Zbl0426.20029MR82j:10041
  11. [HaV] P. de la HARPE et A. VALETTE, La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 75, Soc. Math. de France, 1989. Zbl0759.22001
  12. [Lub] A. LUBOTZKY, Discrete groups, expanding graphs and invariant measures, Progress in Math. 125, Birkhäuser, 1994. Zbl0826.22012MR96g:22018
  13. [LuZ] A. LUBOTZKY and R.J. ZIMMER, Variants of Kazhdan's property for subgroup of semisimple groups, Israel J. of Math., 66 (1989), 289-298. Zbl0706.22010MR90i:22020
  14. [Mar] G.A. MARGULIS, Discrete subgroups of semisimple Lie groups, Springer, 1991. Zbl0732.22008MR92h:22021
  15. [VeK] A.M. VERSHIK and S.I. KARPUSHEV, Cohomology of groups in unitary representations, the neighbourhood of the identity and conditionally positive definite functions, Math. USSR Sbornik, 47 (1984), 513-526. Zbl0528.43005
  16. [Zim] R.J. ZIMMER, Ergodic theory and semisimple groups, Birkhäuser, Boston, 1984. Zbl0571.58015MR86j:22014

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