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Deformed W-algebras in type A for rectangular nilpotent (2004.02737v1)

Published 6 Apr 2020 in math.RT, math-ph, math.MP, and math.QA

Abstract: For any natural numbers n,r, we construct an algebra P_nr 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_nr, 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_nr.

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