Quantizing the Discrete Painlev, VI Equation: The Lax Formalism

A discretization of Painlev, VI equation was obtained by Jimbo and Sakai (Lett Math Phys 38:145-154, 1996). There are two ways to quantize it: (1) use the affine Weyl group symmetry (of ) (Hasegawa in Adv Stud Pure Math 61:275-288, 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.