2015/09/02 by Chris Connell, Connell, Chris, Matilde Martínez +1
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DG #math.DS
paper · pdf · doi:10.48550/arxiv.1509.00695
This paper has been accepted for publication in Transactions of the AMS
arxiv created 2015/09/02 · arxiv updated 2015/09/03
We consider the family of harmonic measures on a lamination L of a compact space X by locally symmetric spaces L of noncompact type, i.e. L≃ ΓL\backslash G/K. We establish a natural bijection between these measures and the measures on an associated lamination foliated by G-orbits, L which are right invariant under a minimal parabolic (Borel) subgroup B < G. In the special case when G is split, these measures correspond to the measures that are invariant under both the Weyl chamber flow and the stable horospherical flows on a certain bundle over the associated Weyl chamber lamination. We also show that the measures on L right invariant under two distinct minimal parabolics, and therefore all of G, are in bijective correspondence with the holonomy-invariant ones.