Uniform distribution of orbits of lattices on spaces of frames

We study distribution of orbits of a lattice Gamma subset of or equal to SL(n, R) in the the space V-n,V-l of l-frames in R-n (1 less than or equal to l less than or equal to n - 1). Examples of dense Gamma-orbits are known from the work of Dani, Raghavan, and Veech. We show that dense orbits of Gamma are uniformly distributed in V-n,V-l with respect to an explicitly described measure. We also establish an analogous result for lattices in Sp(n, R) which act on the space of isotropic n-frames.