Let be an irreducible lattice in a product of simple groups. Assume that has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of in terms of the topology of the dual space of .
We use this result to give a new proof for the triviality of the first cohomology group of with coefficients in a finite dimensional unitary representation.
Soit un réseau irréductible dans un produit de groupes simples. Supposons qu’un des facteurs de possède la propriété (T). Nous donnons une description de la topologie dans un voisinage de la représentation triviale de dimension un de en termes de celle du dual de .
Nous utilisons ce résultat pour donner une nouvelle preuve de l’annulation du premier groupe de cohomologie de à coefficients dans une représentation unitaire de dimension finie.
@article{AIF_1997__47_4_1065_0, author = {Bekka, Mohammed Bachir and Louvet, Nicolas}, title = {On a variant of {Kazhdan's} property {(T)} for subgroups of semisimple groups}, journal = {Annales de l'Institut Fourier}, pages = {1065--1078}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {47}, number = {4}, year = {1997}, doi = {10.5802/aif.1591}, mrnumber = {99b:22019}, zbl = {0874.22006}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1591/} }
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 SP - 1065 EP - 1078 VL - 47 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1591/ DO - 10.5802/aif.1591 LA - en ID - AIF_1997__47_4_1065_0 ER -
%0 Journal Article %A Bekka, Mohammed Bachir %A Louvet, Nicolas %T On a variant of Kazhdan's property (T) for subgroups of semisimple groups %J Annales de l'Institut Fourier %D 1997 %P 1065-1078 %V 47 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1591/ %R 10.5802/aif.1591 %G en %F AIF_1997__47_4_1065_0
Bekka, Mohammed Bachir; Louvet, Nicolas. On a variant of Kazhdan's property (T) for subgroups of semisimple groups. Annales de l'Institut Fourier, Volume 47 (1997) no. 4, pp. 1065-1078. doi : 10.5802/aif.1591. http://archive.numdam.org/articles/10.5802/aif.1591/
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