标题： 六阶Painleve，刚性顶和反射方程 显示英文标题

标题： Painleve VI, Rigid Tops and Reflection Equation

摘要： 我们证明了Painlevé VI方程有一个与非自治Zhukovsky-Volterra陀螺仪等价的形式。 该系统是$C^3$中Euler顶的推广，并包含了附加的陀螺动量常数。 其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。 作为副产品，我们定义了一个具有新边界条件的有限格点上的可积XYZ自旋链。 显示英文摘要

摘要： We show that the Painlev{\'e} VI equation has an equivalent form of the non-autonomous Zhukovsky-Volterra gyrostat. This system is a generalization of the Euler top in $C^3$ and include 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.