JournalsprimsVol. 28 , No. 4DOI 10.2977/prims/1195168205

Principal Fiber Bundle Interpretation of the KP-Hierarchy

  • Josef Dorfmeister

    TU München, Germany
  • Jacek Szmigielski

    University of Kansas, Lawrence, USA
Principal Fiber Bundle Interpretation of the KP-Hierarchy cover

Abstract

The Grassmannian and the Lax pair approaches to the Kadomtsev-Petviashvili (KP) hierarchy are analyzed in the framework of (formal) principal fiber bundles. The underlying factorization problem is formulated as a local triviality condition. In particular the common object in the two approaches — the Baker function — coordinatizes the base space, the fiber consists of certain generalized differential operators. An example is constructed to show that despite the apparent similarity to the splitting in [8], the local triviality condition cannot be given a group theoretic interpretation.