A geometric construction of integrable Hamiltonian hierarchies associated with the classical affine W-algebras

TL;DR

This paper establishes a geometric framework linking classical affine W-algebras to double coset spaces, enabling the construction of integrable Hamiltonian hierarchies that generalize previous principal case results.

Contribution

It introduces a geometric approach to construct integrable hierarchies associated with classical affine W-algebras, extending known results to broader cases.

Findings

Classical affine W-algebras are isomorphic to coordinate rings of double coset spaces.

Integrable Hamiltonian hierarchies are constructed geometrically for these algebras.

The work generalizes previous results by Feigin-Frenkel and Enriquez-Frenkel.

Abstract

A class of classical affine W-algebras are shown to be isomorphic as differential algebras to the coordinate rings of double coset spaces of certain prounipotent proalgebraic groups. As an application, integrable Hamiltonian hierarchies associated with them are constructed geometrically, generalizing the corresponding result of Feigin-Frenkel and Enriquez-Frenkel for the principal cases.