  We obtain a global rigidity result for abelian partially hyperbolic higher
rank actions on certain $2-$step nilmanifolds $X_{\Gamma}$. We show that, under
certain natural assumptions, all such actions are $C^{\infty}-$conjugated to an
affine model. As a consequence, we obtain a centralizer rigidity result,
classifying all possible centralizers for any $C^{1}-$small perturbation of an
irreducible, affine partially hyperbolic map on $X_{\Gamma}$. Along the way, we
also prove two results of independent interest. We describe fibered partially
hyperbolic diffeomorphisms on $X_{\Gamma}$ and we show that topological
conjugacies between partially hyperbolic actions and higher rank affine actions
are $C^{\infty}$.
