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Infinite-Dimensional Flag Manifolds in Integrable Systems

In: Geometric and Algebraic Structures in Differential Equations

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  • G. F. Helminck

    (Universiteit Twente, Department of Mathematics)

  • A. G. Helminck

    (North Carolina State University, Department of Mathematics)

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).

Suggested Citation

  • G. F. Helminck & A. G. Helminck, 1995. "Infinite-Dimensional Flag Manifolds in Integrable Systems," Springer Books, in: P. H. M. Kersten & I. S. Krasil’Shchik (ed.), Geometric and Algebraic Structures in Differential Equations, pages 99-121, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0179-7_6
    DOI: 10.1007/978-94-009-0179-7_6
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