On the spectrum of a large subgroup of a semisimple group

International audienceWe consider a semisimple algebraic group G defined over a local field of zero characteristic and we denote by G the group of its k-rational points. For Gamma a "large" subsemigroup of G we define a closed subgroup associated with Gamma, and we show that is large in a certain sense. This allows us to study the Gamma-orbit closures for certain Gamma-actions. The analytic structure of closed subgroups of G, over R or Q(p), allows us to use the Lie algebras techniques. The properties of the limit set of Gamma are developed; they play an important role in the proofs