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Krichever maps, Faà di Bruno polynomials, and cohomology in KP theory

TitleKrichever maps, Faà di Bruno polynomials, and cohomology in KP theory
Publication TypeJournal Article
Year of Publication1997
AuthorsFalqui, G, Reina, C, Zampa, A
JournalLett. Math. Phys. 42 (1997) 349-361
Abstract

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.

URLhttp://hdl.handle.net/1963/3539
DOI10.1023/A:1007323118991

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