Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers

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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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
Additional Information:This work was supported by a University of Leeds 110 Anniversary Research Scholarship.
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 (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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