Fairon, M. (2019) Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers. Journal of Integrable Systems, 4(1), xyz008. (doi: 10.1093/integr/xyz008)
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Abstract
We study multiplicative quiver varieties associated to specific extensions of cyclic quivers with $m≥2$ vertices. Their global Poisson structure is characterised by quasi-Hamiltonian algebras related to these quivers, which were studied by Van den Bergh for an arbitrary quiver. We show that the spaces are generically isomorphic to the case $m=1$ corresponding to an extended Jordan quiver. This provides a set of local coordinates, which we use to interpret integrable systems as spin variants of the trigonometric Ruijsenaars-Schneider system. This generalises to new spin cases recent works on classical integrable systems in the Ruijsenaars-Schneider family.
Item Type: | Articles |
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Additional Information: | This work was supported by a University of Leeds 110 Anniversary Research Scholarship. |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Fairon, Dr Maxime |
Authors: | Fairon, M. |
Subjects: | Q Science > QA Mathematics |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Journal of Integrable Systems |
Publisher: | Oxford University Press |
ISSN: | 2058-5985 |
ISSN (Online): | 2058-5985 |
Copyright Holders: | Copyright © 2019 The Author |
First Published: | First published in Journal of Integrable Systems 4(1):xyz008 |
Publisher Policy: | Reproduced under a Creative Commons License |
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