Painleve VI, Rigid Tops and Reflection Equation
Quantum Algebra
2009-11-11 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
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 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.
Cite
@article{arxiv.math/0508058,
title = {Painleve VI, Rigid Tops and Reflection Equation},
author = {A. Levin and M. Olshanetsky and A. Zotov},
journal= {arXiv preprint arXiv:math/0508058},
year = {2009}
}
Comments
32 pages, typos corrected