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

Abstract

We study multiplicative quiver varieties associated to specific extensions of cyclic quivers with $m\ge 2$ 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.

arXiv comment40 pages. v2: Added results in subsection 5.6.1

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Cited by in corpus (7)

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• Integrable System of Generalized Relativistic Interacting Tops
• Relativistic interacting integrable elliptic tops
• Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems
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• On the noncommutative Poisson geometry of certain wild character varieties
• Integrable systems on multiplicative quiver varieties from cyclic quivers