Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model

Abstract

We present an algebraic construction of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero–Moser–Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the generalized Hermite (or Hi-Jack) polynomials. The conserved quantities of the rational supersymmetric model are related to their trigonometric relatives through a similarity transformation. This leads to a simple expression between the corresponding eigenfunctions: the generalized Hermite superpolynomials are written as a differential operator acting on the corresponding Jack superpolynomials. As an aside, the maximal superintegrability of the supersymmetric rational Calogero–Moser–Sutherland model is demonstrated.