Painlevé VI, Rigid Tops and Reflection Equation
Painlevé VI, Rigid Tops and Reflection Equation
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Painlevé VI、刚性顶部和反射方程
DOI：
10.1007/s00220-006-0089-y
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发表时间：
2005
影响因子：
2.4
通讯作者：
Andrei Vladimirovich Zotov
中科院分区：
文献类型：
--
作者：
A. Levin;M. Olshanetsky;Andrei Vladimirovich Zotov
本文证明了Painlevé VI方程具有非自治Zhukovsky-Volterra陀螺仪的等价形式。该系统是欧拉顶的推广，
$$\mathbb{C}^3$$并包括附加的恒定陀螺仪动量。它的自治版本的量子化是通过反射方程实现的。相应的二次代数推广了Sklyanin代数。作为副积，我们定义了有限格上可积的XYZ自旋链，并给出了新的边界条件。
AbstractWe show that the Painlevé VI equation has an equivalent form of the non-autonomous Zhukovsky-Volterra gyrostat. This system is a generalization of the Euler top in
$$\mathbb{C}^3$$ and includes the additional constant gyrostat momentum. The quantization of its autonomous version is achieved by the reflection equation. The corresponding quadratic algebra generalizes the Sklyanin algebra. As by product we define integrable XYZ spin chain on a finite lattice with new boundary conditions.
影响因子：
1.4
作者：
A. Khovanskii;A. Varchenko;V. Vassiliev;Y. Manin
通讯作者：
A. Khovanskii;A. Varchenko;V. Vassiliev;Y. Manin