Explicit formulae for the generalized Hermite polynomials in superspace

Abstract

We provide explicit formulae for the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero–Moser–Sutherland model with harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in superspace. The construction relies on the triangular action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions.