We consider solutions of the matrix Kadomtsev-Petviashvili (KP) hierarchy that are trigonometric functions of the first hierarchical time t₁ = x and establish the correspondence with the spin generalization of the trigonometric Calogero-Moser system at the level of hierarchies. Namely, the evolution of poles x_i and matrix residues at the poles a ^α_i b ^β_i of the solutions with respect to the kth hierarchical time of the matrix KP hierarchy is shown to be given by the Hamiltonian flow with the Hamiltonian which is a linear combination of the first k higher Hamiltonians of the spin trigonometric Calogero-Moser system with coordinates x_i and with spin degrees of freedom α ^α_i and b ^β_i . By considering the evolution of poles according to the discrete time matrix KP hierarchy, we also introduce the integrable discrete time version of the trigonometric spin Calogero-Moser system.

中文翻译：

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矩阵Kadomtsev-Petviashvili层次结构和三角Calogero-Moser层次结构的自旋推广

我们考虑矩阵Kadomtsev-Petviashvili（KP）层次结构的解决方案，它们是第一层次时间t ₁ = x的三角函数，并在层次结构级别上与三角Calogero-Moser系统的自旋泛化建立了对应关系。即，磁极的进化X_我和基质的残基在两极一个^α_我b ^β_我的解决方案相对于所述ķ矩阵KP层次的第分层时间被示出为通过与哈密顿哈密顿流动，这是给出前k个线性组合 自旋三角函数卡洛杰罗-Moser的系统坐标的更高汉密尔顿X_我并与自旋自由度α ^α_我和b ^β_我。通过根据离散时间矩阵KP层次考虑极点的演化，我们还介绍了三角自旋Calogero-Moser系统的可积分离散时间版本。