## Advanced Studies in Pure Mathematics

### A quantization of the sixth Painlevé equation

Hajime Nagoya

#### 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

Dates
Revised: 25 March 2008
First available in Project Euclid: 28 November 2018

https://projecteuclid.org/ euclid.aspm/1543447916

Digital Object Identifier
doi:10.2969/aspm/05510291

Mathematical Reviews number (MathSciNet)
MR2463505

Zentralblatt MATH identifier
1185.34138

#### 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