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Explicit formulas for the generalized Hermite polynomials in superspace

Patrick Desrosiers·Luc Lapointe·Pierre Mathieu
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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.

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Patrick Desrosiers, Luc Lapointe, Pierre Mathieu. 2003-10-31. Explicit formulas for the generalized Hermite polynomials in superspace. https://doi.org/10.1088/0305-4470%2F37%2F4%2F013

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