τ-Functions for a two-point version of the KP-hierarchy

G.F. Helminck

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    Abstract

    In this paper a multipoint version of the linearization of the KP-hierarchy is described. Solutions of this system in the form of wave functions are constructed starting from a suitable Grassmann manifold and a group of commuting flows corresponding to the configuration of n points in C. The failure of equivariance at lifting these flows to the determinant bundle over this Grassmann manifold is measured by the determinants of certain Fredholm operators, the so-called τ-functions. In the case of two points an explicit relation between these τ-functions and the wave functions is derived.
    Original languageEnglish
    Pages (from-to)367-383
    JournalIndagationes mathematicae
    Volume14
    Issue number3-4
    DOIs
    Publication statusPublished - 2003

    Keywords

    • Multipoint KP-hierarchy
    • Grassmann manifold
    • τ-functions

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