Deformed W-algebras as Symmetries of Generalized Integrable Hierarchies

TL;DR

This paper presents a unified framework linking the Hamiltonian structures of integrable hierarchies to W-algebras, demonstrating that these structures can be viewed as deformations of W-algebras, thus deepening understanding of their symmetries.

Contribution

It provides an explicit formula connecting integrable hierarchies' Hamiltonian structures with deformations of W-algebras, offering a novel unified perspective.

Findings

Hamiltonian structures are shown to be deformations of W-algebras.

Explicit formula relating integrable hierarchies and W-algebras.

Unified description of symmetries in integrable systems.

Abstract

A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be understood as a deformation of the latter.