Calogero-Moser Models. II Symmetries and Foldings
Calogero-Moser Models. II Symmetries and Foldings
复制标题
卡洛杰罗-莫泽模型。
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
K. Takasaki
中科院分区：
文献类型：
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作者：
A. Bordner;Ryu Sasaki;K. Takasaki
提出了基于简单花边根系(包括E8)的CalogeroMoser模型的通用Lax对(根型和最小型)。它们的存在有光谱参数和没有光谱参数，它们适用于所有四种位势的选择：有理、三角、双曲和椭圆。对于椭圆势，简单花边模型的离散对称性源于扩展的动态图的自同构，它与势的周期性相结合得到了一类CalogeroMoser模型，称为扭曲的非简单花边模型。对于无扭非简单花边模型，导出了两种根型Lax对(基于长根和短根)，它们分别包含长根和短根的独立耦合常数。BCN模型包含三个独立的耦合，分别用于长根、中根和短根。基于长根的G2模型呈现出一个值得进一步研究的新特点。
Universal Lax pairs (the root type and the minimal type) are presented for CalogeroMoser models based on simply laced root systems, including E8. They exist with and without spectral parameters and they work for all of the four choices of potentials: the rational, trigonometric, hyperbolic and elliptic. For the elliptic potential, the discrete symmetries of the simply laced models, originating from the automorphism of the extended Dynkin diagrams, are combined with the periodicity of the potential to derive a class of CalogeroMoser models known as the ‘twisted non-simply laced models’. For untwisted non-simply laced models, two kinds of root type Lax pairs (based on long roots and short roots) are derived which contain independent coupling constants for the long and short roots. The BCn model contains three independent couplings, for the long, middle and short roots. The G2 model based on long roots exhibits a new feature which deserves further study.