Uniform distribution of orbits of lattices on spaces of frames

2003/10/16 by Alexander Gorodnik, Gorodnik, Alexander
Mathematics · #Advanced Algebra and Geometry #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #math.DS #msc:22E40 #msc:37A15 #msc:37A17

paper · pdf · doi:10.48550/arxiv.math/0310235

To be published in Duke Math. Journal, 31 pages

arxiv created 2003/10/16 · arxiv updated 2009/12/01

Abstract

We study distribution of orbits of a lattice Γ<SL(n,R) in the the space V_n,l of l-frames in Rⁿ (1≤ l≤ n-1). Examples of dense Γ-orbits are known from the work of Dani, Raghavan, and Veech. We show that dense orbits of Γare uniformly distributed in V_n,l with respect to an explicitly described measure. We also establish analogous result for lattices in Sp(n,R) that act on the space of isotropic n-frames.

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