no. 4
On a variant of Kazhdan's property (T) for subgroups of semisimple groups
Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1065-1078.

Soit Γ un réseau irréductible dans un produit G de groupes simples. Supposons qu’un des facteurs de G possède la propriété (T). Nous donnons une description de la topologie dans un voisinage de la représentation triviale de dimension un de Γ en termes de celle du dual G ^ de G .

Nous utilisons ce résultat pour donner une nouvelle preuve de l’annulation du premier groupe de cohomologie de Γ à coefficients dans une représentation unitaire de dimension finie.

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.

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     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},
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     mrnumber = {99b:22019},
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     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1591/}
}
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Bekka, Mohammed Bachir; Louvet, Nicolas. On a variant of Kazhdan's property (T) for subgroups of semisimple groups. Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1065-1078. doi : 10.5802/aif.1591. https://aif.centre-mersenne.org/articles/10.5802/aif.1591/

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