Advanced Studies in Pure Mathematics

A quantization of the sixth Painlevé equation

Hajime Nagoya

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Abstract

The sixth Painlevé equation has the affine Weyl group symmetry of type $D_{4}^{(1)}$ as a group of Bäcklund transformations and is written as a Hamiltonian system. We propose a quantization of the sixth Painlevé equation with the extended affine Weyl group symmetry of type $D_{4}^{(1)}$.

Article information

Source
Noncommutativity and Singularities: Proceedings of French–Japanese symposia held at IHÉS in 2006, J.-P. Bourguignon, M. Kotani, Y. Maeda and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 291-298

Dates
Received: 2 August 2007
Revised: 25 March 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543447916

Digital Object Identifier
doi:10.2969/aspm/05510291

Mathematical Reviews number (MathSciNet)
MR2463505

Zentralblatt MATH identifier
1185.34138

Subjects
Primary: 34M55: Painlevé and other special equations; classification, hierarchies; 37K35: Lie-Bäcklund and other transformations 39A99: None of the above, but in this section 81S99: None of the above, but in this section

Keywords
Quantization Painlevé equation affine Weyl group symmetry

Citation

Nagoya, Hajime. A quantization of the sixth Painlevé equation. Noncommutativity and Singularities: Proceedings of French–Japanese symposia held at IHÉS in 2006, 291--298, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05510291. https://projecteuclid.org/euclid.aspm/1543447916


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