Quiver W-algebras

TL;DR

This paper introduces a new class of gauge-theory K-theoretic W-algebras associated with quivers, establishing their connection to qq-characters and operator formalism, with potential applications in advanced algebraic structures.

Contribution

It generalizes existing W-algebra definitions to arbitrary quivers and links gauge-theoretic qq-characters to operator formalism, expanding the mathematical framework.

Findings

Defined gauge-theory K-theoretic W-algebras for quivers.

Proved isomorphism between qq-characters and operator formalism.

Suggested applications to generalized Borcherds-Kac-Moody algebras.

Abstract

For a quiver with weighted arrows we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al., and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds-Kac-Moody Lie algebras, their quantum affinizations and associated W-algebras.