Differential equations compatible with kz equations

被引：24

作者：

Felder G. ^{[1
]}

Markov Y. ^{[2
]}

Tarasov V. ^{[3
]}

Varchenko A. ^{[2
]}

机构：

[1] Departement Mathematik, ETH-Zentrum

[2] Department of Mathematics, University of North Carolina, Chapel Hill

[3] St. Petersburg Branch of Steklov Mathematical Institute, St. Petersburg, 191011

来源：

Mathematical Physics, Analysis and Geometry | 2000年 / 3卷 / 2期

基金：

美国国家科学基金会;

关键词：

Hypergeometric solutions; Kac-moody lie algebras; Kz equations;

D O I：

10.1023/A:1009862302234

中图分类号：

学科分类号：

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 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. © 2000 Kluwer Academic Publishers.

引用

页码：139 / 177

页数：38

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