Proximality and equidistribution on the Furstenberg boundary
Abstract
Let G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and a lattice in G. We prove that every -orbits in the Furstenberg boundary G/P is equidistributed for the averages over Riemannian balls. The proof is based on the proximality of the action of on G/P.
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