Local rigidity of algebraic partially hyperboilc actions.

We consider a broad class of partially hyperbolic algebraic ctions of higher-rank abelian groups. Those actions appear as restrictions of full Cartan actions on homogeneous spaces of Lie groups and their factors by compact subgroups of the centralizer. The common property of those actions is that hyperbolic directions generate the whole tangent space. For these actions we prove differentiable rigidity for perturbations of sufficiently high regularity. The method of proof is KAM type iteration scheme.