On Diff(S^1) Covariantization Of Pseudodifferential Operator

Abstract

A study of diff($S^1$) covariant properties of pseudodifferential operator of integer degree is presented. First, it is shown that the action of diff($S^1$) defines a hamiltonian flow defined by the second Gelfand-Dickey bracket if and only if the pseudodifferential operator transforms covariantly. Secondly, the covariant form of a pseudodifferential operator of degree n not equal to 0, 1, -1 is constructed by exploiting the inverse of covariant derivative. This, in particular, implies the existence of primary basis for W_{KP}^{(n)} (n not equal to 0, 1, -1).

20 pages

References in corpus (2)

• 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

Cited by in corpus (5)

• Classical Extended Conformal Algebras Associated with Constrained KP Hierarchy
• d=2, N=2 Superconformally Covariant Operators and Super W-Algebras
• Conformal Covariantization of Moyal-Lax Operators
• Nonlocal extended conformal algebras associated with multi-constraint KP hierarchy and their free-field realizations
• Classical N=2 W-superalgebras From Superpseudodifferential Operators