2017/04/19 by Oleg Chalykh, Maxime Fairon · 40 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Context (archaeology) #Gauge theory #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Multiplicative function #Nonlinear Waves and Solitons #Phase space #Physics #Pure mathematics #Quantum mechanics #Quiver #math-ph #math.MP #math.QA
paper · pdf · doi:10.1016/j.geomphys.2017.08.006
published in Journal of Geometry and Physics 121, 413-437 (Elsevier BV) · 27 pages
arxiv created 2017/04/19 · openalex publication_date 2017/08/18 · arxiv updated 2018/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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, as well as in the context of the Macdonald theory.