## Advanced Studies in Pure Mathematics

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

Koji Hasegawa

#### 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

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