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.

arXiv commentv2: 15 pages, accepted in Nonlinearity

References in corpus (22)

• Integrable spin Calogero-Moser systems
• Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models
• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
• Degenerate Integrability of Spin Calogero-Moser Systems and the duality with the spin Ruijsenaars systems
• Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers
• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• Algebraic Linearization of Dynamics of Calogero Type for any Coxeter Group
• Quasi-compact Higgs bundles and Calogero-Sutherland systems with two types spins
• New infinite families of $N$th-order superintegrable systems separating in Cartesian coordinates
• Superintegrable systems and Riemann-Roch theorem
• On the superintegrability of the rational Ruijsenaars-Schneider model
• Notes on the vector adelic Grassmannian
• On a family of quivers related to the Gibbons-Hermsen system
• Sutherland Models for Complex Reflection Groups
• Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals
• Spin Calogero models and dynamical r-matrices
• A new way to classify 2D higher order quantum superintegrable systems
• Algebra of Dunkl Laplace-Runge-Lenz vector
• Generalized spin Sutherland systems revisited
• Integrable many-body systems of Calogero-Ruijsenaars type
• Canonical spectral coordinates for the Calogero-Moser space associated with the cyclic quiver

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