Jack superpolynomials, superpartition ordering and determinantal formulas

Details Jack superpolynomials, superpartition ordering and determinantal formulas Jack superpolynomials, superpartition ordering and determinantal formulas

2001-05-11

arxiv.org/abs/hep-th/0105107v2

Commun.Math.Phys. 233 (2003) 383-402

Physics

High Energy Physics

High Energy Physics - Theory

20 pages - minor corrections; to appear in CMP

Scientific paper

10.1007/s00220-002-0731-2

We call superpartitions the indices of the eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model. We obtain an ordering on superpartitions from the explicit action of the model's Hamiltonian on monomial superfunctions. This allows to define Jack superpolynomials as the unique eigenfunctions of the model that decompose triangularly, with respect to this ordering, on the basis of monomial superfunctions. This further leads to a simple and explicit determinantal expression for the Jack superpolynomials.

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