Abstract
Let Gamma be a lattice in G = SL(n, R) and X = G/S be a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establish the uniform distribution of orbits of Gamma in X analogous to the classical equidistribution on a torus. To obtain this result, we first prove an ergodic theorem along balls in the connected component of a Borel subgroup of G.
Translated title of the contribution | Lattice action on the boundary of SL(n,R) |
---|---|
Original language | English |
Pages (from-to) | 1817-1837 |
Number of pages | 21 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 23 |
Issue number | 6 |
DOIs | |
Publication status | Published - Dec 2003 |