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arXiv · 2207.08054

Tau functions, infinite Grassmannians and lattice recurrences

S. Arthamonov·J. Harnad·J. Hurtubise
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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.

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S. Arthamonov, J. Harnad, J. Hurtubise. 2022-07-17. Tau functions, infinite Grassmannians and lattice recurrences. https://doi.org/10.1063/5.0110404

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