We extend the middle convolution for monodromy of Fuchsian ordinary differential equations due to Katz to an operation for monodromy of KZ equations. This operation, also called the middle convolution, gives a monodromy of KZ equation obtained by the additive middle convolution. Since the fundamental group of the domain of definition of KZ equation is the pure braid group, our middle convolution also gives a recursive way of constructing irreducible representations of the pure braid group. Several applications are considered.

中文翻译：

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KZ 方程的乘法中间卷积

我们将由于 Katz 引起的 Fuchsian 常微分方程单项的中间卷积扩展到 KZ 方程的单项操作。该操作也称为中间卷积，给出了由加性中间卷积获得的 KZ 方程的单项性。由于 KZ 方程定义域的基本群是纯编织群，我们的中间卷积也给出了构造纯编织群不可约表示的递归方式。考虑了几种应用。