We study smooth factors of the standard actions of lattices in higher-rank semisimple Lie groups on flag manifolds. Under a mild condition on the existence of a single differentiable sink, we show that these factors are –conjugate to the standard actions on flag manifolds.
"Smooth factors of projective actions of higher-rank lattices and rigidity." Geom. Topol. 22 (2) 1227 - 1266, 2018. https://doi.org/10.2140/gt.2018.22.1227