Limit distributions of expanding translates of certain orbits on homogeneous spaces

Details Limit distributions of expanding translates of certain orbits on homogeneous spaces Limit distributions of expanding translates of certain orbits on homogeneous spaces

2000-02-22

arxiv.org/abs/math/0002184v1

Proc. Indian Acad. Sci. Math. Sci. 106 (1996), no. 2, 105--125

Mathematics

Representation Theory

Scientific paper

Let L be a Lie group and Lambda a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L, and the image of G on L/Lambda is dense. Let c be a diagonalizable element of G not contained in a compact subgroup. Let U be the expanding horospherical subgroup of G associated to c. Let Omega be a nonempty open subset of U, and {n_i} be a sequence of natural numbers tending to infinity. It is shown that the image of the union of the sets c^{n_i}.Omega in L/Lambda is dense. A stronger measure theoretic formulation of this result is also obtained. Among other applications of the above result, we describe G-equivariant topological factors of the product space L/Lambda \times G/P, where the real rank of G is greater than 1, P is a parabolic subgroup of G, and G acts diagonally. We also describe equivariant topological factors of unipotent flows on finite volume homogeneous spaces of Lie groups.

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