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Letters in Mathematical Physics

, Volume 42, Issue 4, pp 349–361 | Cite as

Krichever Maps, Faà di Bruno Polynomials, and Cohomology in KP Theory

  • Gregorio Falqui
  • Cesare Reina
  • Alessandro Zampa
Article

Abstract

We study the geometrical meaning of the Faà 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 Faà 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.

KP hierarchy Faà di Bruno pdynomials hypercohomology groups. 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Gregorio Falqui
    • 1
  • Cesare Reina
    • 1
  • Alessandro Zampa
    • 1
  1. 1.SISSA/ISASTriesteItaly

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