The Algebra of Differential Operators on the Circle and $W_{KP}^{(q)}$

Abstract

Radul has recently introduced a map from the Lie algebra of differential operators on the circle to $W_n$. In this note we extend this map to $W_{KP}^{(q)}$, a recently introduced one-parameter deformation of $W_{KP}$---the second hamiltonian structure of the KP hierarchy. We use this to give a short proof that $W_{\infty }$ is the symmetry algebra of additional symmetries of the KP equation.

12 pages, Plain TeX, BONN-HE-92/34, KUL-TF-92/27, QMW-PH-92-20 (v3: solved legacy compilation problems)

References in corpus (5)

• Additional symmetries of KP, Grassmannian, and the string equation
• A One-Parameter Family of Hamiltonian Structures for the KP Hierarchy and a Continuous Deformation of the Nonlinear $\W_{\rm KP}$ Algebra
• The Topography of $\W_\infty$-Type Algebras
• A geometrical interpretation of classical W-transformations
• The Super W_\INFTY Symmetry of the Manin-Radul Super KP Hierarchy

Cited by in corpus (3)

• The algebra of q-pseudodifferential symbols and the q-W_{KP}^n algebra
• Additional Symmetries of Supersymmetric KP Hierarchies
• Bihamiltonian Reductions and W_n Algebras