Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models
Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models
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乘法箭袋品种和广义 Ruijsenaars-Schneider 模型
DOI：
10.1016/j.geomphys.2017.08.006
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发表时间：
2017
影响因子：
1.5
通讯作者：
Chalykh O
中科院分区：
文献类型：
--
作者：
Chalykh O
研究了具有m个顶点的（扩展）循环颤振的若干与乘型颤振自然相关的经典可积系统。我们的可积系统的相空间是通过准哈密顿化简从颤振的表示空间得到的。构造了三族泊松交换函数，并在适当的达布坐标下显式地表示出来。当m= 1时，对应于蝌蚪振动和Ruijsenaars-Schneider系统及其变体，而对于m= 1，我们得到了推广Ruijsenaars-Schneider系统的新的可积系统。这些系统及其量子版本最近也出现在超对称规范理论和环切DAHAs的背景下（Braverman等人[32,34,35]和Kodera和Nakajima bb0），以及麦克唐纳理论的背景下（Chalykh和Etingof， 2013）。
We study some classical integrable systems naturally associated with multiplicative quiver varieties for the (extended) cyclic quiver with m vertices. The phase space of our integrable systems is obtained by quasi-Hamiltonian reduction from the space of representations of the quiver. Three families of Poisson-commuting functions are constructed and written explicitly in suitable Darboux coordinates. The case m= 1 corresponds to the tadpole quiver and the Ruijsenaars–Schneider system and its variants, while for m> 1 we obtain new integrable systems that generalise the Ruijsenaars–Schneider system. These systems and their quantum versions also appeared recently in the context of supersymmetric gauge theory and cyclotomic DAHAs (Braverman et al.[32, 34, 35] and Kodera and Nakajima [36]), as well as in the context of the Macdonald theory (Chalykh and Etingof, 2013).