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

Global rigidity for some partially hyperbolic abelian actions with 1-dimensional center