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Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group.

Shalom, Yehuda — 2000

Annals of Mathematics. Second Series

Bounded generation and Kazhdan’s property $(T)$

Yehuda Shalom — 1999

Publications Mathématiques de l'IHÉS

Explicit Kazhdan constants for representations of semisimple and arithmetic groups

Yehuda Shalom — 2000

Annales de l'institut Fourier

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 $Γ \cap B_{r}$ , where $B_{r} \subset G$ is a ball of radius $r$ , and the dependence of $r$ on $Γ$ is described explicitly....

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