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Lattice action on the boundary of SL(n,R)

Alexander Gorodnik
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Abstract

Let Γbe a lattice in G=SL(n,R) and X=G/S 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 uniform distribution of orbits of Γin X analogous to the classical equidistribution on torus. To obtain this result, we first prove an ergodic theorem along balls in the connected component of Borel subgroup of G.

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Alexander Gorodnik. 2003-10-16. Lattice action on the boundary of SL(n,R). https://arxiv.org/abs/math/0310233

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