Uniform distribution of orbits of lattices on spaces of frames

Abstract

We study distribution of orbits of a lattice Γ<SL(n,R) in the the space V_{n,l} of l-frames in R^n (1\le l\le 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.