The generalized Giambelli formula and polynomial KP and CKP tau-functions

Abstract

The first part of the paper is devoted to two descriptions of all polynomial tau-functions of the KP hierarchy: by a generalized Jacobi-Trudy formula, and a generalized Giambelli formula. We use the latter formula in the second part to obtain all polynomial tau-functions of the CKP hierarchy and its n-reductions. In particular, for n=3 we find all polynomial tau-functions of the Kaup-Kupershmidt hierarchy.

arXiv comment32 pages

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• Equilibrium of Charges and Differential Equations Solved by Polynomials II