Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie Algebra $D_4$

Abstract

We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra $D_4$ 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 to them such as recurrence relations and generating functions.

17 pages, no figures

References in corpus (1)

• An elementary construction of lowering and raising operators for the trigonometric Calogero-Sutherland model

Cited by in corpus (3)

• On an approach for computing the generating functions of the characters of simple Lie algebras
• Quantum trigonometric Calogero-Sutherland model, irreducible characters and Clebsch-Gordan series for the exceptional algebra E7
• Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra E6