TY - JOUR

T1 - Quantizing the Discrete Painlevé VI Equation

T2 - The Lax Formalism

AU - Hasegawa, Koji

N1 - Funding Information:
The author is supported by the Grant-in-Aid for Scientific Research (Kakenhi) C, 23540004. Part of this paper is based on a lecture delivered at University of Tokyo, 2007, and the author is grateful to Professor Jimbo Michio and Professor Jun-ichi Shiraishi for their hospitality. Thanks are also due to Professor Gen Kuroki, Professor Yasuhiko Yamada, and (especially) Professor Akihiro Tsuchiya for their kind interest.

PY - 2013/8

Y1 - 2013/8

N2 - 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(1)5 (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.

AB - 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(1)5 (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.

KW - Weyl groups

KW - discrete Painlevé equations

KW - quantum integrable systems

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U2 - 10.1007/s11005-013-0620-y

DO - 10.1007/s11005-013-0620-y

M3 - Article

AN - SCOPUS:84878859920

SN - 0377-9017

VL - 103

SP - 865

EP - 879

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 8

ER -