W-Algebra Symmetries of Generalised Drinfel'd-Sokolov Hierarchies

TL;DR

This paper demonstrates that W-algebra transformations serve as symmetries for generalized Drinfel'd-Sokolov hierarchies, with examples including KdV, Boussinesque, and Polyakov-Bershadsky hierarchies.

Contribution

It establishes the role of W-algebra symmetries in these hierarchies using zero-curvature formulation, highlighting their significance in integrable systems.

Findings

W-algebra transformations are symmetries of the hierarchies

Illustrations with KdV, Boussinesque, and Polyakov-Bershadsky hierarchies

Zero-curvature formulation confirms symmetry properties

Abstract

Using the zero-curvature formulation, it is shown that W-algebra transformations are symmetries of corresponding generalised Drinfel'd-Sokolov hierarchies. This result is illustrated with the examples of the KdV and Boussinesque hierarchies, and the hierarchy associated to the Polyakov-Bershadsky W-algebra.