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

TL;DR

This paper introduces generalized Calogero models invariant under infinite affine, hyperbolic, and Lorentzian Weyl groups, providing explicit formulas for Coxeter element actions to formulate these models.

Contribution

It develops new Calogero models with invariance under infinite Weyl groups and derives explicit formulas for Coxeter element actions on roots.

Findings

Formulated Calogero models with infinite Weyl group invariance

Derived explicit Coxeter element action formulas

Extended models to affine, hyperbolic, and Lorentzian cases

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.