On Procesi bundles

TL;DR

This paper classifies Procesi bundles on symplectic resolutions obtained via Hamiltonian reduction, linking them to tautological bundles and exploring their relation to Symplectic reflection algebras.

Contribution

It provides a classification of Procesi bundles on certain symplectic resolutions and connects them to tautological bundles and Symplectic reflection algebras.

Findings

Classification of Procesi bundles on Hamiltonian reductions

Relation established between Procesi bundles and tautological bundles

Connection made between Procesi bundles and Symplectic reflection algebras

Abstract

Procesi bundles are certain vector bundles on symplectic resolutions of symplectic quotient singularities for wreath-products of the symmetric groups with Kleinian groups. Roughly speaking, we can define Procesi bundles as bundles on resolutions that provide derived McKay equivalence. In this paper we classify Procesi bundles on resolutions obtained by Hamiltonian reduction and relate the Procesi bundles to the tautological bundles on the resolutions. Our proofs are based on deformation arguments and a connection of Procesi bundles with Symplectic reflection algebras.