Principal Fiber Bundle Interpretation of the KP-Hierarchy

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.