Chalykh, O and Fairon, M (2017) Multiplicative quiver varieties and generalised Ruijsenaars–Schneider models. Journal of Geometry and Physics, 121. pp. 413-437. ISSN 0393-0440
Abstract
We study some classical integrable systems naturally associated with multiplicative quiver varieties for the (extended) cyclic quiver with m vertices. The phase space of our integrable systems is obtained by quasi-Hamiltonian reduction from the space of representations of the quiver. Three families of Poisson-commuting functions are constructed and written explicitly in suitable Darboux coordinates. The case m = 1 corresponds to the tadpole quiver and the Ruijsenaars–Schneider system and its variants, while for m > 1 we obtain new integrable systems that generalise the Ruijsenaars–Schneider system. These systems and their quantum versions also appeared recently in the context of supersymmetric gauge theory and cyclotomic DAHAs (Braverman et al. [32,34,35] and Kodera and Nakajima [36]), as well as in the context of the Macdonald theory (Chalykh and Etingof, 2013).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Elsevier B.V. This is an author produced version of a paper published in Journal of Geometry and Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Quivers; Noncommutative geometry; Double Poisson brackets; Quasi-Hamiltonian reduction; Ruijsenaars–Schneider system |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/K004999/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Aug 2017 09:11 |
Last Modified: | 18 Aug 2018 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.geomphys.2017.08.006 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:120450 |