与KZ方程相容的微分方程
Differential Equations Compatible with KZ Equations
摘要：
我们定义了一个系统的“动态”微分方程兼容的KZ微分方程。KZ微分方程与复简单李代数$\mathbf{g}$相关联。这些是关于$n$复变数$z_i$的函数的方程，该函数在$n$有限维$\mathbf{g}$ -模块的张量积中取值。KZ方程依赖于$\mathbf{g}$的Cartan子代数中的“对偶”变量。动力学微分方程是关于对偶变量的微分方程。我们证明了KZ方程的标准超几何解也满足动力学方程。作为应用，我们给出了超几何解基坐标的一个新的行列式公式。
英文摘要：
We define a system of "dynamical" differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra $\mathbf{g}$. These are equations on a function of $n$ complex variables $z_i$ taking values in the tensor product of $n$ finite dimensional $\mathbf{g}$-modules. The KZ equations depend on the "dual" variable in the Cartan subalgebra of $\mathbf{g}$. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions.
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