Infinite-dimensional flag manifolds in integrable systems

G.F. Helminck, A.G. Helminck

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    Abstract

    In this paper, we present several instances where infinite-dimensional flag varieties and their holomorphic line bundles play a role in integrable systems. As such, we give the correspondence between flag varieties and Darboux transformations for the KP hierarchy and the nth KdV hierarchy. We construct solutions of the nth MKdV hierarchy from the space of periodic flags and we treat the geometric interpretation of the Miura transform. Finally, we show how the group extension connected with these line bundles shows up at integrable deformations of linear systems on ℙ1(ℂ).
    Original languageUndefined
    Pages (from-to)99-121
    JournalActa applicandae mathematicae
    Volume41
    Issue number1
    DOIs
    Publication statusPublished - 1995

    Keywords

    • IR-97360

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