Infinite affine, hyperbolic and Lorentzian Weyl groups with their associated Calogero models

Abstract

We propose generalizations of Calogero models that exhibit invariance with respect to the infinite Weyl groups of affine, hyperbolic, and Lorentzian types. Our approach involves deriving closed analytic formulas for the action of the associated Coxeter elements of infinite order acting on arbitrary roots within their respective root spaces. These formulas are then utilized in formulating the new type of Calogero models.

arXiv comment25 pages

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Cited by in corpus (2)

• A Calogero Model with root string representatives of infinite order Coxeter orbits
• Toda field theories and Calogero models associated to infinite Weyl groups