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

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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

Scientific paper

10.1016/0370-2693(94)01518-H

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 r\^ole 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.

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