Realizations of Affine Weyl Group Symmetries on the Quantum Painlevé Equations by Fractional Calculus
Realizations of Affine Weyl Group Symmetries on the Quantum Painlevé Equations by Fractional Calculus
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DOI：
10.1007/s11005-012-0557-6
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发表时间：
2012-03
影响因子：
1.2
通讯作者：
H. Nagoya
中科院分区：
文献类型：
--
作者：
H. Nagoya
用分数阶微积分实现了量子Painlevé方程薛定谔方程的仿射Weyl群对称性。这种实现使我们能够构造无限多个量子Painlevé方程的薛定谔方程的超几何解。换言之，由于量子Painlevé方程的薛定谔方程等价于Knizhnik-Zamolodchikov方程，我们给出了一种构造Knizhnik-Zamolodchikov方程超几何解的方法。
We realize affine Weyl group symmetries on the Schrödinger equations for the quantum Painlevé equations, by fractional calculus. This realization enables us to construct an infinite number of hypergeometric solutions to the Schrödinger equations for the quantum Painlevé equations. In other words, since the Schrödinger equations for the quantum Painlevé equations are equivalent to the Knizhnik–Zamolodchikov equations, we give one method of constructing hypergeometric solutions to the Knizhnik–Zamolodchikov equations.