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 Kadomtsev-Petviashvili (KP) hierarchy: by a generalized Jacobi-Trudi 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 we find all polynomial tau-functions of the Kaup-Kupershmidt hierarchy.