Infinite-Dimensional Flag Manifolds in Integrable Systems

G. F. Helminck () and A. G. Helminck ()
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G. F. Helminck: Universiteit Twente, Department of Mathematics
A. G. Helminck: North Carolina State University, Department of Mathematics

A chapter in Geometric and Algebraic Structures in Differential Equations, 1995, pp 99-121 from Springer

Abstract: 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).

Keywords: Line Bundle; Darboux Transformation; Deformation Function; Grassmann Manifold; Deformation Space (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0179-7_6

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DOI: 10.1007/978-94-009-0179-7_6

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