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

Patrick Desrosiers·Luc Lapointe·Pierre Mathieu
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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.

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Patrick Desrosiers, Luc Lapointe, Pierre Mathieu. 2003-09-06. Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model. https://doi.org/10.1016/j.nuclphysb.2003.08.003

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