A non-homogeneous orbit of a diagonal subgroup

François Maucourant (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Let G=SL(n,R) with n>5. We construct examples of lattices Gamma of G, subgroup A of the diagonal group and points x in G/Gamma such that the closure of the orbit Ax is not homogeneous but does not factors through the action of a one-parameter non-unipotent group. This contradicts a conjecture of Margulis.

Mots clés: homogeneous dynamics; diagonal group

Domaines: Systèmes dynamiques [math.DS]

François Maucourant. A non-homogeneous orbit of a diagonal subgroup. Annals of Mathematics, 2010, 171 (1), pp.557-570. ⟨hal-00164251v2⟩