Deformed W-algebras in Type A for Rectangular Nilpotent

Abstract

For any n,r∈N, we construct an algebra Prn via generators and quadratic relations, and show that it deforms the W–algebra of glnr with respect to a nilpotent with Jordan block decomposition r+…+r. We introduce a surjective morphism from half of the quantum toroidal algebra of gln to Prn, and show that the action of the quantum toroidal algebra on the K–theory groups of the moduli spaces of parabolic sheaves factors through Prn.