In this paper, we show that four sets of differential Fay identities of an N-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wavefunctions. From this, we derive the Lax representation for the N-component KP hierarchy, which are equations satisfied by some pseudo-differential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in Date et al (1981 J. Phys. Soc. Japan 50 3806-12), we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in Takebe (2002 Lett. Math. Phys. 59 157-72).
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机译：在本文中，我们表明，从由层次结构的tau函数满足的双线性关系导出的N分量KP层次结构的四组差分Fay身份足以推导波浪函数的辅助线性方程。由此，我们得出了N分量KP层次的Lax表示，这是一些具有矩阵系数的伪微分算子所满足的方程。除了在Date等（1981 J. Phys。Soc。Japan 50 3806-12）中提出的关于时间变量的Lax方程之外，我们还获得了一组与不同电荷扇区有关的方程，可以将其视为Takebe（2002 Lett。Math。Phys。59 157-72）中提出的修改后的KP层次结构。
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