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.

32 pages

References in corpus (5)

• Kadomtsev-Petviashvili turning points and CKP hierarchy
• Polynomial KP and BKP $\tau$-functions and correlators
• BKP tau-functions as square roots of KP tau-functions
• Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations
• Tau functions, infinite Grassmannians and lattice recurrences

Cited by in corpus (1)

• Equilibrium of Charges and Differential Equations Solved by Polynomials II