Advanced Studies in Pure Mathematics

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 discrete Painlevé VI equation as a discrete Hamiltonian flow commuting with the action of $W (D_4^{(1)})$.

Article information

Source
Exploring New Structures and Natural Constructions in Mathematical Physics, K. Hasegawa, T. Hayashi, S. Hosono and Y. Yamada, eds. (Tokyo: Mathematical Society of Japan, 2011), 275-288

Dates
Received: 27 February 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543085349

Digital Object Identifier
doi:10.2969/aspm/06110275

Mathematical Reviews number (MathSciNet)
MR2867149

Zentralblatt MATH identifier
1241.81114

Citation

Hasegawa, Koji. Quantizing the Bäcklund transformations of Painlevé equations and the quantum discrete Painlevé VI equation. Exploring New Structures and Natural Constructions in Mathematical Physics, 275--288, Mathematical Society of Japan, Tokyo, Japan, 2011. doi:10.2969/aspm/06110275. https://projecteuclid.org/euclid.aspm/1543085349


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