A non-homogeneous orbit of a diagonal subgroup

2007/07/19 by François Maucourant, Maucourant, François
Mathematics · #22E40 #37B99 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:22E40 #msc:37B99

paper · pdf · doi:10.48550/arxiv.0707.2920

arxiv created 2008/08/28 · arxiv updated 2009/12/01

Abstract

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.

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