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Quantizing the Bäcklund transformations of Painlevé equations and the quantum discrete Painlevé VI equation

Koji Hasegawa
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Abstract

Based on the works by Kajiwara, Noumi and Yamada, we propose a canonically quantized version of the rational Weyl group representation which originally arose as "symmetries" or the Bäcklund transformations in Painlevé equations. We thereby propose a quantization of the discrete Painlevé VI equation as a discrete Hamiltonian flow commuting with the action of $W(D_4^{(1)})$.

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Koji Hasegawa. 2007-03-01. Quantizing the Bäcklund transformations of Painlevé equations and the quantum discrete Painlevé VI equation. https://arxiv.org/abs/math/0703036

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