q-PainleveV I equation arising fromq-UC hierarchy
q-PainleveV I equation arising fromq-UC hierarchy
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由 q-UC 层次结构产生的 q-PainleveV I 方程
DOI：
10.1098/rspa.2019.0299
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
T. Masuda
中科院分区：
文献类型：
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作者：
Teruhisa Tsuda;T. Masuda
通过考虑A（1）1和A（1）3型反射子群的正规化子，可以从（A3×A1×A1）（1）型子根系构造出两个子群：和.这两种对称性是在离散Painlevé方程的研究中出现的（Kajiwara K，Noumi M，Yamada Y. 2002年q-Painlevé系统产生的q-KP层次。Math.Phys.62，259-268; Takenawa T. 2003 Q-Painlevé V方程D（1）5型Weyl群对称性. 46，173-186; Okubo N，Suzuki T. 2018广义q-Painlevé VI系统的类型（A2 n +1+A1+A1）（1）产生于集群代数。(http：//arxiv.org/abs/quant-ph/1810.03252）），其中显示出某些无限阶的非平移元素产生离散的Painlevé方程。我们澄清了这些元素的性质，在柯克斯特群的规范化的Brink-Howlett理论（Howlett RB。1980反射群的抛物子群的正规化子。J.伦敦数学学会。（2）21，62-80; Brink B，Howlett RB. 1999 Coxeter群中抛物子群的正规化子。Math.136，323-351）。这是第一个一系列的研究，调查的性质，离散可积方程通过理论的正规化。
By considering the normalizers of reflection subgroups of typesA(1)1andA(1)3in, two subgroups:andcan be constructed from a (A3×A1×A1)(1)type subroot system. These two symmetries arose in the studies of discrete Painlevé equations (Kajiwara K, Noumi M, Yamada Y. 2002q-Painlevé systems arising fromq-KP hierarchy.Lett. Math. Phys.62, 259–268; Takenawa T. 2003 Weyl group symmetry of typeD(1)5in theq-Painlevé V equation.Funkcial. Ekvac.46, 173–186; Okubo N, Suzuki T. 2018 Generalizedq-Painlevé VI systems of type (A2n+1+A1+A1)(1)arising from cluster algebra. (http://arxiv.org/abs/quant-ph/1810.03252)), where certain non-translational elements of infinite order were shown to give rise to discrete Painlevé equations. We clarify the nature of these elements in terms of Brink-Howlett theory of normalizers of Coxeter groups (Howlett RB. 1980 Normalizers of parabolic subgroups of reflection groups.J. London Math. Soc. (2)21, 62–80; Brink B, Howlett RB. 1999 Normalizers of parabolic subgroups in Coxeter groups.Invent. Math.136, 323–351). This is the first of a series of studies which investigates the properties of discrete integrable equations via the theory of normalizers.