Multiplicative quiver varieties and generalised Ruijsenaars–Schneider models - INSPIRE

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Multiplicative quiver varieties and generalised Ruijsenaars–Schneider models

Apr 19, 2017

25 pages

Published in:

J.Geom.Phys. 121 (2017) 413-437

Published: Nov, 2017

e-Print:

1704.05814 [math.QA]

DOI:

10.1016/j.geomphys.2017.08.006

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Abstract: (Elsevier)

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).

Note:

27 pages

70H06
53D20
16G20
83C65
Quivers
Noncommutative geometry
Double Poisson brackets
Quasi-Hamiltonian reduction
Ruijsenaars–Schneider system

References(53)

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