Krichever Maps, Faa' di Bruno Polynomials, and Cohomology in KP Theory

Details Krichever Maps, Faa' di Bruno Polynomials, and Cohomology in KP Theory Krichever Maps, Faa' di Bruno Polynomials, and Cohomology in KP Theory

1997-04-15

arxiv.org/abs/solv-int/9704010v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, LaTex using amssymb.sty. To be published in Lett. Math. Phys

Scientific paper

We study the geometrical meaning of the Faa' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faa' di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.

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