Deformed W-algebras in type A for rectangular nilpotent

2020/04/06 by Neguţ, Andrei
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2004.02737

Abstract

For any natural numbers n,r, we construct an algebra P_n^r via generators and quadratic relations, and show that it deforms the W-algebra of gl_nr with respect to a nilpotent with Jordan block decomposition r+...+r. We introduce a surjective morphism from half of the quantum toroidal algebra of gl_n to P_n^r, and show that the action of the quantum toroidal algebra on the K-theory groups of the moduli spaces of parabolic sheaves factors through P_n^r.

Related

• Toward AGT for parabolic sheaves
• Deformations of \mathcal W algebras via quantum toroidal algebras
• K-theoretic Hall algebras, quantum groups and super quantum groups
• Quadratic relations of the deformed W-algebra
• Quantum toroidal and shuffle algebras