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Displaying similar documents to “An example of a generalized completely continuous representation of a locally compact group”

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

Mohammed Bachir Bekka, Nicolas Louvet (1997)

Annales de l'institut Fourier

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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.

Explicit Kazhdan constants for representations of semisimple and arithmetic groups

Yehuda Shalom (2000)

Annales de l'institut Fourier

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Consider a simple non-compact algebraic group, over any locally compact non-discrete field, which has Kazhdan’s property ( T ) . For any such group, G , we present a Kazhdan set of two elements, and compute its best Kazhdan constant. Then, settling a question raised by Serre and by de la Harpe and Valette, explicit Kazhdan constants for every lattice Γ in G are obtained, for a “geometric” generating set of the form Γ ∩ B r , where B r ⊂ G is a ball of radius r , and the dependence of r on Γ is described...