Centrally Extended W_{1+\infty} and the KP Hierarchy

Abstract

It is well known that the centerless W_{1+\infty} algebra provides a hamiltonian structure for the KP hierarchy. In this letter we address the question whether the centerful version plays a similar rôle in any related integrable system. We find that, surprisingly enough, the centrally extended W_{1+\infty} algebra yields yet another Poisson structure for the same standard KP hierarchy. This is proven by explicit construction of the infinitely many new hamiltonians in closed form.

10 pages, plain tex (all macros included), US-FT-17-94, (some AMS fonts have been skipped for easier TEXing)

References in corpus (4)

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• Wormholes in Two Dimensional Dilaton Gravity