Consider homogeneous and , for an -algebraic group . A lattice acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors, and joinings defined a priori only in the measurable category are in fact algebraically constrained. Arguing in an elementary fashion, we manage to classify all the measurable commuting with the -action: assuming ergodicity, we find that they are algebraically defined.
"Rigidity of group actions on homogeneous spaces, III." Duke Math. J. 164 (1) 115 - 155, 15 January 2015. https://doi.org/10.1215/00127094-2860021