Differential Equations Compatible with KZ Equations
Differential Equations Compatible with KZ Equations
复制标题
与 KZ 方程兼容的微分方程
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
A. Varchenko
中科院分区：
文献类型：
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作者：
Giovanni Felder;Y. Markov;V. Tarasov;A. Varchenko
我们定义了一个系统的“动力学”微分方程兼容的KZ微分方程。KZ微分方程对应于一个复单李代数g。这些是关于n个复变量zi的函数的方程，取值于n个有限维g-模的张量积。KZ方程依赖于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。
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 g. These are equations on a function of n complex variables zi taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the ‘dual’ variable in the Cartan subalgebra of 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.