Isomorphisms of quantizations via quantization of resolutions

Understand

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.