Joinings of higher-rank diagonalizable actions on locally homogeneous spaces

Abstract

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 $\mathbb{R}$-split torus on $G/\Gamma$ with $G$ a simple Lie group of $\mathbb{R}$-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