Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra D4

We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra D4 in terms of a set of Weyl-invariant variables, namely, the characters of the fundamental representations of the Lie algebra. This parametrization allows us to solve for the energy eigenfunctions of the theory and to study properties of the system of orthogonal polynomials associated with them such as recurrence relations and generating functions