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.
Keywords
Cite
@article{arxiv.hep-th/0305038,
title = {Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model},
author = {Patrick Desrosiers and Luc Lapointe and Pierre Mathieu},
journal= {arXiv preprint arXiv:hep-th/0305038},
year = {2015}
}
Comments
Latex 2e, shortened version, one reference added, 18 pages