Exactly solvable potentials of Calogero type for q-deformed Coxeter groups

We establish that by parametrizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the previously introduced notion of solvability which consists of relating the Hamiltonian to finite-dimensional representation spaces of a Lie algebra. We present explicitly the Gq2-case for which we construct the potentials by means of suitable gauge transformations