A One-Parameter Family of Hamiltonian Structures for the KP Hierarchy and a Continuous Deformation of the Nonlinear $\W_{\rm KP}$ Algebra

Abstract

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting $\W$-algebra is a one-parameter deformation of $\W_{\rm KP}$ admitting a central extension for generic values of the parameter, reducing naturally to $\W_n$ for special values of the parameter, and contracting to the centrally extended $\W_{1+\infty}$, $\W_\infty$ and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic to $\w_{\rm KP}$. The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of $\widehat{\W}_\infty$ which contracts to a new nonlinear algebra of the $\W_\infty$-type.

31 pages, compressed uuencoded .dvi file, BONN-HE-92/20, US-FT-7/92, KUL-TF-92/20. [version just replaced was truncated by some mailer]

References in corpus (3)

• W-symmetry in Conformal Field Theory
• Nonlinear ${\hat{W}}_{\infty }$ Current Algebra in the SL(2,R)/U(1) Coset Model
• The Classical Limit of W-Algebras

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