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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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 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. |
| Status: | Published |
| Refereed: | Yes |
| 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: | 0951-7715 |
| 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 |
| Related URLs: |
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