Abstract
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.
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Research Fellow of the Japan Society for the Promotion of Science.
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Nagoya, H. Realizations of Affine Weyl Group Symmetries on the Quantum Painlevé Equations by Fractional Calculus. Lett Math Phys 102, 297–321 (2012). https://doi.org/10.1007/s11005-012-0557-6
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DOI: https://doi.org/10.1007/s11005-012-0557-6