Quantizing the Discrete Painlevé VI Equation: The Lax Formalism

Author： Hasegawa Koji  

Publisher： Springer Publishing Company

ISSN： 0377-9017

Source： Letters in Mathematical Physics, Vol.103, Iss.8, 2013-08, pp. : 865-879

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Abstract

A discretization of Painlevé 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 $${D_5^{(1)}}$$ ) (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.

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