Joinings of higher rank torus actions on homogeneous spaces

TL;DR

This paper proves that any joining of higher rank torus actions on certain arithmetic quotients must have an algebraic structure, revealing rigidity in these dynamical systems.

Contribution

It establishes that all joinings of higher rank torus actions on S-arithmetic quotients are necessarily algebraic, advancing understanding of their rigidity properties.

Findings

Joinings are algebraic in these systems.

Higher rank torus actions exhibit rigidity.

Results apply to S-arithmetic quotients of algebraic groups.

Abstract

We show that joinings of higher rank torus actions on S-arithmetic quotients of semi-simple or perfect algebraic groups must be algebraic.