Symmetries of Quantum Lax Equations for the Painlevé Equations

被引：0
作者：
Hajime Nagoya
Yasuhiko Yamada
机构：
[1] Kobe University,Department of Mathematics
来源：
Annales Henri Poincaré | 2014年 / 15卷
关键词：
Automorphism Group; Commutation Relation; Weyl Group; Dynkin Diagram; Gauge Factor;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Based on the fact that the Painlevé equations can be written as Hamiltonian systems with affine Weyl group symmetries, a canonical quantization of the Painlevé equations preserving such symmetries has been studied recently. On the other hand, since the Painlevé equations can also be described as isomonodromic deformations of certain second-order linear differential equations, a quantization of such Lax formalism is also a natural problem. In this paper, we introduce a canonical quantization of Lax equations for the Painlevé equations and study their symmetries. We also show that our quantum Lax equations are derived from Virasoro conformal field theory.
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页码：313 / 344
页数：31
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共 41 条
[1]  
Alday L.F.(2010)Liouville correlation functions from four-dimensional Gauge Theories Lett. Math. Phys. 91 167-197
[2]  
Gaiotto D.(1984)Infinite conformal symmetry in two-dimensional quantum field theory Nucl. Phys. B 241 333-380
[3]  
Tachikawa Y.(1981)Monodromy preserving deformation of linear ordinary differential equations with rational coefficients II. Physica 2D 407-448
[4]  
Belavin A.A.(2008)Remarks on the confuent KZ equation for $${\mathfrak{sl_2}}$$ and quantum Painlevé equations J. Phys. A Math. Theor. 41 175205-160
[5]  
Polyakov A.M.(2005)Cubic Pencils and Painlevé Hamiltonians Funkcialaj Ekvacioj 48 147-3421
[6]  
Zamolodchikov A.B.(2010)Generalized Okubo systems and the middle convolution Int. Math. Res. Not. 17 3394-1031
[7]  
Jimbo M.(2004)Quantum Painlevé systems of type Int. J. Math. 15 1007-423
[8]  
Miwa T.(2008)Quantum Painlevé equations: from continuous to discrete and back Regul. Chaotic Dyn. 13 417-298
[9]  
Jimbo M.(2009)A quantization of the sixth Painlevé equation, noncommutativity and singularities Adv. Stud. Pure Math. 55 291-321
[10]  
Nagoya H.(2010)Confluent primary fields in the conformal field theory J. Phys. A Math. Theor. 43 465203-1496
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