Two-component symplectic universal characters and integrable hierarchies

Abstract

In this paper, we first construct a symplectic Schur function solution to a newly defined two-component symplectic Kadomtsev–Petviashvili hierarchy. As a generalization of a two-component symplectic Schur function, we construct two-component symplectic universal characters which satisfy quadratic equations in an infinite-dimensional integrable dynamic system called a two-component symplectic universal character hierarchy. Then, we define a modified symplectic universal character hierarchy whose tau function can be represented by free fermions in Clifford algebras.