## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- 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

### A quantization of the sixth Painlevé equation

#### 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**

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