Superintegrability of Calogero-Moser systems associated with the cyclic quiver

Fairon, M. and Görbe, T. (2021) Superintegrability of Calogero-Moser systems associated with the cyclic quiver. Nonlinearity, 34(11), pp. 7662-7682. (doi: 10.1088/1361-6544/ac2674)

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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 An−1 and Bn, 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.

Item Type:Articles
Additional Information:The work of M.F. was partly supported by a Rankin-Sneddon Research Fellowship of the University of Glasgow.
Glasgow Author(s) Enlighten ID:Fairon, Dr Maxime
Authors: Fairon, M., and Görbe, T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Nonlinearity
Publisher:IOP Publishing
ISSN (Online):1361-6544
Published Online:29 September 2021
Copyright Holders:Copyright © 2021 IOP Publishing Ltd and London Mathematical Society
First Published:First published in Nonlinearity 34(11): 7662-7682
Publisher Policy:Reproduced under a Creative Commons licence
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