Rigidity of group actions on homogeneous spaces, III

Abstract

Consider homogeneous G/H and G/F, for an S-algebraic group G. A lattice Γ acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors and joinings defined apriori only in the measurable category are in fact algebraically constrained. Arguing in an elementary fashion we manage to classify all the measurable Φ commuting with the Γ-action: assuming ergodicity, we find they are algebraically defined.

References in corpus (1)

• Invariant Measures and Orbit Closures on Homogeneous Spaces for Actions of Subgroups Generated by Unipotent Elements

Cited by in corpus (2)

• Boundaries, rigidity of representations, and Lyapunov exponents
• Charmenability of higher rank arithmetic groups