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Property (T) and A ¯ 2 groups

Donald I. Cartwright, Wojciech Młotkowski, Tim Steger (1994)

Annales de l'institut Fourier

We show that each group Γ in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of Γ with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers...

Regular trace formula and base change for G L ( n )

Yuval Z. Flicker (1990)

Annales de l'institut Fourier

The “regular”trace formula, for a test function with a local component which is Iwahori-biinvariant and sufficiently regular with respect to the other components, is developed in the context of a reductive group. It is used to give a simple proof of the theory of base-change for cuspidal automorphic representations of G L ( n ) which have a supercuspidal component. A purely local proof is given to transfer orbital integrals of sufficiently many spherical functions, by relating them to regular Iwahori functions....

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