KdV type hierarchies, The string equation and W1+infinity constraints

J.W. van de Leur, Johan van de Leur

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    To every partition n = n1 + n2 + + ns one can associate a vertex operator realization of the Lie algebras α∞ and . Using this construction we make reductions of the s-component KP hierarchy, reductions which are related to these partitions. In this way we obtain matrix KdV type equations. Now assuming that (1) τ is a τ-function of the [n1, n2, …, ns]th reduced KP hierarchy and (2) τ satisfies a ‘natural’ string equation, we prove that τ also satisfies the vacuum constraints of the W1+∞ algebra.
    Original languageUndefined
    Pages (from-to)95-124
    Number of pages30
    JournalJournal of geometry and physics
    Issue number17
    Publication statusPublished - 1995


    • KdV hierarchies
    • IR-29757
    • METIS-140391
    • Strings

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