Quantizing the discrete Painlevé VI equation : The Lax formalism

Abstract

A discretization of Painlevé VI equation was obtained by Jimbo and Sakai in 1996. There are two ways to quantize it: 1) use the affine Weyl group symmetry (of $D_5^{(1)}$) (Hasegawa, 2011), 2) Lax formalism i.e. monodromy preserving point of view. It turns out that the second approach is also successful and gives the same quantization as in the first approach.

14 pages with 4 figures

References in corpus (2)

• Reductions of lattice mKdV to $q$-${\mathrm{P}}_{VI}$
• Discrete Painlevé equations and their Lax pairs as reductions of integrable lattice equations

Cited by in corpus (1)

• Variations of $q$-Garnier system