Divergence exponentielle des groupes discrets en rang supérieur

Abstract

Let G be a real semisimple Lie group with finite center, a a Cartan subspace of the Lie algebra of G and a +⊂ a a closed Weyl chamber in a . To a discrete Zariski dense subgroup Γ of G we associate an homogeneous function ψ Γ: a +→ R ∪ {−∞} which generalizes the exponent of convergence of Γ, usually considered in R -rank 1. We show that this function is concave then we deduce some constructions of Patterson measures for Γ.