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 -