AI 中文总结
研究约束矩阵 KP 层次，将其视为多分量 KP 层次特殊约化，给出双线性方程，利用多分量玻色子 - 费米子对应构造 tau 函数，不借助拟行列式导出解。
AI 中文摘要
从 tau 函数方面研究约束矩阵 KP 层次$(L^{k})_{<0}=\sum_{i=1}^{m}Q_{i}\partial^{-1}R_{i}^{\intercal}$。首先将矩阵 KP 层次视为多分量 KP 层次的一种特殊约化，然后给出其作为多分量 KP 层次的双线性方程，最后基于这些结果利用多分量玻色子 - 费米子对应构造约束矩阵 KP 层次的 tau 函数，且不使用拟行列式导出其解。
英文摘要
The constrained matrix KP hierarchy $(L^{k})_{<0}=\sum_{i=1}^{m}Q_{i}\partial^{-1}R_{i}^{\intercal}$ is investigated from the aspects of tau functions. Firstly, the matrix KP hierarchy is viewed as one special reduction of the multi-component KP hierarchy. Then bilinear equations of the constrained matrix KP hierarchy as the multi-component KP hierarchy are given in terms of tau functions. Finally based upon these results, the tau functions for the constrained matrix KP hierarchy are constructed by using the multi-component boson-fermion correspondence. Notice that the solutions of the constrained matrix KP hierarchy are derived without using quasi-determinants.
Comments22 pages
