  The goal of this paper is to establish Beilinson-Bernstein type localization
theorems for quantizations of some conical symplectic resolutions. We prove the
full localization theorems for finite and affine type A Nakajima quiver
varieties. The proof is based on two partial results that hold in more general
situations. First, we establish an exactness result for global section functor
if there is a tilting generator that has a rank 1 summand. Second, we examine
when the global section functor restricts to an equivalence between categories
$\mathcal{O}$.
