Non-crystallographic reduction of generalized Calogero-Moser models

Abstract

We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero-Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is recovered. For the Hamiltonians of trigonometric, hyperbolic and elliptic type, we obtain novel integrable dynamical systems with a second potential term which is rescaled by the golden ratio. We explicitly show for the simplest of these non-crystallographic models how the corresponding classical equations of motion can be derived from a Lie algebraic Lax pair based on the larger, crystallographic Coxeter group.

arXiv comment21 pages

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Cited by in corpus (4)

• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• Antilinear deformations of Coxeter groups, an application to Calogero models
• G(2)-Calogero-Moser Lax operators from reduction
• Sutherland Models for Complex Reflection Groups