  We show local and cocycle rigidity for $\R^k \times \Z^l$ partially
hyperbolic translation actions on homogeneous spaces $\mc G/ \Lambda$. We
consider a large class of actions whose geometric properties are more
complicated than previously treated cases. It is also the first time that
partially hyperbolic twisted symmetric space examples have been treated in the
literature. The main new ingredient in the proof is a combination of geometric
method and the theory of central extensions.
