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

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 n=3

Automated summary

The first part of the paper presents two descriptions of all polynomial tau-functions of the Kadomtsev-Petviashvili (KP) hierarchy: a generalized Jacobi-Trudi formula and a generalized Giambelli formula. In the second part, the latter formula is used to obtain all polynomial tau-functions of the CKP hierarchy and its n-reductions. Specifically, for n=3...