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arXiv · 2101.05520

Superintegrability of Calogero-Moser systems associated with the cyclic quiver

Maxime Fairon·Tamás Görbe
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Abstract

We study complex integrable systems on quiver varieties associated with the cyclic quiver, and prove their superintegrability by explicitly constructing first integrals. We interpret them as rational Calogero-Moser systems endowed with internal degrees of freedom called spins. They encompass the usual systems in type $A_{n-1}$ and $B_n$, as well as generalisations introduced by Chalykh and Silantyev in connection with the multicomponent KP hierarchy. We also prove that superintegrability is preserved when a harmonic oscillator potential is added.

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Maxime Fairon, Tamás Görbe. 2021-01-14. Superintegrability of Calogero-Moser systems associated with the cyclic quiver. https://doi.org/10.1088/1361-6544/ac2674

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