Polynomial Tau Functions of Symplectic KP and Multi-component Symplectic KP Hierarchies

In this paper, we prove that a zero mode of an appropriate combinatorial generating function is a polynomial tau-function of a form of symplectic KP (SKP) hierarchy and extend it to the multi-component SKP hierarchy. Moreover, we write the polynomial tau-function of SKP hierarchy as determinant form in terms of the Vandermonde-like identity.

Automated summary

This paper proves that the zero mode of an appropriate combinatorial generating function is a polynomial tau-function of a symplectic KP hierarchy, and extends it to the multi-component SKP hierarchy. Moreover, the polynomial tau-function of the SKP hierarchy is written as a determinant form using the Vandermonde-like identity.