GEOMETRY AND CLASSIFICATION OF SOLUTIONS OF THE CLASSICAL DYNAMICAL YANG-BAXTER EQUATION
GEOMETRY AND CLASSIFICATION OF SOLUTIONS OF THE CLASSICAL DYNAMICAL YANG-BAXTER EQUATION
复制标题
经典动态Yang-Baxter方程解的几何和分类
DOI：
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发表时间：
1997
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：
P. Etingof;A. Varchenko
经典的杨-巴克斯特方程(CEBE)是可积系统理论中的核心代数方程。它的解决方案被Belavin和Drinfeld分类。Cybe的量子化导致了量子群理论的产生。Drinfeld给出了Cybe的几何解释，并由此产生了PoissonLie群理论。经典的动力学Yang-Baxter方程(CDYBE)是一个类似于Cybe的重要的微分方程，由Feld提出，作为环面上关联函数的微分Knizhnik-Zamolodchikov-Bernard方程的相容条件。CDYBE的量子化使费尔德引入了一种有趣的椭圆形量子群类似物。很明显，许多与Cybe有关的重要概念和结果都有动力学上的相似之处。本文对CDYBE的解进行了分类，并给出了CDYBE的几何解释。分类和解释与Belavin-Drinfeld的图像非常相似。0.引言0.1.1984年，Knizhnik和Zamolodchikov证明了单李代数g的Wess-Zumino-Witten(WZW)共形场理论P上的共形块的关联函数满足微分方程组
The classical Yang-Baxter equation (CYBE) is an algebraic equation central in the theory of integrable systems. Its solutions were classified by Belavin and Drinfeld. Quantization of CYBE led to the theory of quantum groups. A geometric interpretation of CYBE was given by Drinfeld and gave rise to the theory of PoissonLie groups. The classical dynamical Yang-Baxter equation (CDYBE) is an important differential equation analagous to CYBE and introduced by Felder as the consistency condition for the differential Knizhnik-Zamolodchikov-Bernard equations for correlation functions in conformal field theory on tori. Quantization of CDYBE allowed Felder to introduce an interesting elliptic analog of quantum groups. It becomes clear that numerous important notions and results connected with CYBE have dynamical analogs. In this paper we classify solutions to CDYBE and give geometric interpretation to CDYBE. The classification and interpretation are remarkably analogous to the Belavin-Drinfeld picture. 0.Introduction 0.1. In 1984 Knizhnik and Zamolodchikov showed that correlation functions of conformal blocks on P for the Wess-Zumino-Witten (WZW) conformal field theory for a simple Lie algebra g satisfy the differential equations