Joinings of higher-rank diagonalizable actions on locally homogeneous spaces

摘要

We classify joinings between a fairly general class of higher-rank diagonalizable actions on locally homogeneous spaces. In particular, we classify joinings of the action of a maximal R-split torus on G / Gamma with G a simple Lie group of R-rank at least 2 and Gamma < G a lattice. We deduce from this a classification of measurable factors of such actions as well as certain equidistribution properties.