  In this paper we prove the existence of isomorphisms between certain
non-commutative algebras that are interesting from representation theoretic
perspective and arise as quantizations of certain Poisson algebras. We show
that quantizations of Kleinian resolutions obtained by three different
constructions are isomorphic to each other. The constructions are via
symplectic reflection algebras, quantum Hamiltonian reduction, and W-algebras.
Next, we prove that parabolic W-algebras in type A are isomorphic to quantum
Hamiltonian reductions associated to quivers of type A. Finally, we show that
the symplectic reflection algebras for wreath-products of the symmetric group
and a Kleinian group are isomorphic to certain quantum Hamiltonian reductions.
Our results involving W-algebras are new, while for those dealing with
symplectic reflection algebras we just give new proofs. A key ingredient in our
proofs is the study of quantizations of symplectic resolutions of appropriate
Poisson varieties.
