Superintegrability of Calogero-Moser systems associated with the cyclic quiver

Abstract

We study complex integrable systems on quiver varieties associated with the cyclic quiver, and prove their superintegrability by explicitly constructing first integrals. We interpret them as rational Calogero-Moser systems endowed with internal degrees of freedom called spins. They encompass the usual systems in type $A_{n-1}$ and $B_n$, as well as generalisations introduced by Chalykh and Silantyev in connection with the multicomponent KP hierarchy. We also prove that superintegrability is preserved when a harmonic oscillator potential is added.

v2: 15 pages, accepted in Nonlinearity

References in corpus (4)

• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• Superintegrable systems and Riemann-Roch theorem
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Cited by in corpus (5)

• Many-body integrable systems implied by WLZZ models
• Integrable multi-Hamiltonian systems from reduction of an extended quasi-Poisson double of $U(n)$
• Integrable systems on multiplicative quiver varieties from cyclic quivers
• On the maximal superintegrability of strongly isochronous Hamiltonians
• Functorial constructions related to double Poisson vertex algebras