Tau functions, infinite Grassmannians and lattice recurrences

Abstract

The addition formulae for KP $\tau$-functions, when evaluated at lattice points in the KP flow group orbits in the infinite dimensional Sato-Segal-Wilson Grassmannian, give infinite parametric families of solutions to discretizations of the KP hierarchy. The CKP hierarchy may similarly be viewed as commuting flows on the Lagrangian sub-Grassmannian of maximal isotropic subspaces with respect to a suitably defined symplectic form. Evaluating the $\tau$-functions at a sublattice of points within the KP orbit, the resulting discretization gives solutions both to the hyperdeterminantal relations (or Kashaev recurrence) and the hexahedron (or Kenyon-Pemantle) recurrence.

arXiv comment57 pages. Acknowledgements added

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Cited by in corpus (2)

• The generalized Giambelli formula and polynomial KP and CKP tau-functions
• Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations