Local rigidity of generalized quasi-affine actions for higher-rank groups

Let $G$ be a semi-simple Lie group with no compact factors and no simple factors isomorphic to $SO(1,n)$ or $SU(1,n)$, and let $\Gamma<G$ be a lattice. A generalized quasi-affine action is understood in the sense used in the paper. Local rigidity conjecture. Any volume preserving generalized quasi-affine action of $G$ or $\Gamma$ on a compact manifold is locally rigid. This proposes a common generalization of local rigidity results for higher-rank actions and remains a direction for future research; the source gives no resolution.