Publications of the Research Institute for Mathematical Sciences


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Volume 28, Issue 4, 1992, pp. 503–533
DOI: 10.2977/prims/1195168205

Published online: 1992-08-31

Principal Fiber Bundle Interpretation of the KP-Hierarchy

Josef Dorfmeister[1] and Jacek Szmigielski[2]

(1) TU München, Germany
(2) University of Kansas, Lawrence, USA

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.

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Dorfmeister Josef, Szmigielski Jacek: Principal Fiber Bundle Interpretation of the KP-Hierarchy. Publ. Res. Inst. Math. Sci. 28 (1992), 503-533. doi: 10.2977/prims/1195168205