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.

中文翻译：

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二元辛通用字符和可积层次

在本文中，我们首先为新定义的双分量辛 Kadomtsev-Petviashvili 层次构造了一个辛 Schur 函数解。作为二元辛 Schur 函数的推广，我们构造了二元辛全能字符，该二元辛全能字符满足无限维可积动态系统中的二次方程，称为二元辛全能字符层次。然后，我们定义了一个修正的辛通用字符层次，其 tau 函数可以用 Clifford 代数中的自由费米子表示。