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We propose generalizations of Calogero models that exhibit invariance withrespect to the infinite Weyl groups of affine, hyperbolic, and Lorentziantypes. Our approach involves deriving closed analytic formulas for the actionof the associated Coxeter elements of infinite order acting on arbitrary rootswithin their respective root spaces. These formulas are then utilized informulating the new type of Calogero models.

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