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

Shalom, Yehuda

Displaying similar documents to “Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group.”

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

Geometric constructions and representations

Wolf, Joseph A.

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[For the entire collection see Zbl 0742.00067.]Let $G$ be a connected semisimple Lie group with finite center. In this review article the author describes first the geometric realization of the discrete series representations of $G$ on Dolbeault cohomology spaces and the tempered series of representations of $G$ on partial Dolbeault cohomology spaces. Then he discusses his joint work with Wilfried Schmid on the construction of maximal globalizations of standard Zuckerman modules via geometric...