Explicit formulas for the generalized Hermite polynomials in superspace

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.

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

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• The Calogero-Sutherland Model and Generalized Classical Polynomials
• The Calogero Model - Anyonic Representation, Fermionic Extension and Supersymmetry
• Super Lax Pairs and Infinite Symmetries in The $1/r^2$ System
• Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
• Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement
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• Jack polynomials in superspace
• Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model
• Jack superpolynomials, superpartition ordering and determinantal formulas

Cited by in corpus (6)

• A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type
• Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Explicit formulas for the eigenfunctions of the N-body Calogero model
• An Explicit Formula for Symmetric Polynomials Related to the Eigenfunctions of Calogero-Sutherland Models
• Symmetric functions in superspace