KP hierarchy for the cyclic quiver
KP hierarchy for the cyclic quiver
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DOI：
10.1063/1.4991031
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发表时间：
2017-07-01
影响因子：
1.3
通讯作者：
Silantyev, Alexey
中科院分区：
文献类型：
--
作者：
Chalykh, Oleg;Silantyev, Alexey
我们介绍了一个概括的KP层次结构，密切相关的循环和Cherednik代数H-k（Z（m））。这个层次结构取决于m个参数（其中一个可以被删除），通常的KP层次结构对应于m = 1的情况。Wilson [Invent.]的结果。133（1），1-41（1998）]，我们表明，我们的层次承认的解决方案参数化适当的numerous品种。这些解决方案的极点动力学被证明是由经典的Calogero-Moser系统的花环产品Z（m）（sic）S-n和它的新的自旋版本。这些结果被进一步推广到多分量层次的情况下。由AIP出版社出版。
We introduce a generalisation of the KP hierarchy, closely related to the cyclic quiver and the Cherednik algebra H-k(Z(m)). This hierarchy depends on m parameters (one of which can be eliminated), with the usual KP hierarchy corresponding to the m = 1 case. Generalising the result of Wilson [Invent. Math. 133(1), 1-41 (1998)], we show that our hierarchy admits solutions parameterised by suitable quiver varieties. The pole dynamics for these solutions is shown to be governed by the classical Calogero-Moser system for the wreath-product Z(m) (sic) S-n and its new spin version. These results are further extended to the case of the multi-component hierarchy. Published by AIP Publishing.