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Polynomially growing pluriharmonic functions on Siegel domains

Monika Gilżyńska (2007)

Colloquium Mathematicae

Let 𝓓 be a symmetric type two Siegel domain over the cone of positive definite Hermitian matrices and let N(Φ)S be a solvable Lie group acting simply transitively on 𝓓. We characterize polynomially growing pluriharmonic functions on 𝓓 by means of three N(Φ)S-invariant second order elliptic degenerate operators.

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...

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