Displaying similar documents to “Property (T) and A ¯ 2 groups”

Eigenfunctions of the Laplace operators for buildings of type B ~ 2

A. M. Mantero, A. Zappa (2002)

Bollettino dell'Unione Matematica Italiana

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We consider for an affine building of type B ~ 2 Helgason's conjecture with respect to Laplace operators defined over different types of vertices. We prove that there are cases in which the conjecture fails, since there exist eigenfunctions which are not the Poisson transform of finitely additive measures at the maximal boundary of the building.

Macdonald formula for spherical functions on affine buildings

A. M. Mantero, A. Zappa (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we explicitly determine the Macdonald formula for spherical functions on any locally finite, regular and affine Bruhat-Tits building, by constructing the finite difference equations that must be satisfied and explaining how they arise, by only using the geometric properties of the building.

Estimates for simple random walks on fundamental groups of surfaces

Laurent Bartholdi, Serge Cantat, Tullio Ceccherini-Silberstein, Pierre de la Harpe (1997)

Colloquium Mathematicae

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Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.

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...