Explicit formulas for the generalized Hermite polynomials in superspace
High Energy Physics - Theory
2008-11-26 v2 Combinatorics
Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
We provide explicit formulas 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.
Cite
@article{arxiv.hep-th/0309067,
title = {Explicit formulas for the generalized Hermite polynomials in superspace},
author = {Patrick Desrosiers and Luc Lapointe and Pierre Mathieu},
journal= {arXiv preprint arXiv:hep-th/0309067},
year = {2008}
}
Comments
19 pages. This is a recasting of the second part of the first version of hep-th/0305038 which has been splitted in two articles. In this revised version, the introduction has been rewritten and a new appendix has been added. To appear in JPA