Bounded generation and Kazhdan’s property
Explicit Kazhdan constants for representations of semisimple and arithmetic groups
Consider a simple non-compact algebraic group, over any locally compact non-discrete field, which has Kazhdan’s property . For any such group, , 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 in are obtained, for a “geometric” generating set of the form , where is a ball of radius , and the dependence of on is described explicitly....
Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group.
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