Jack superpolynomials: physical and combinatorial definitions

Details Jack superpolynomials: physical and combinatorial definitions Jack superpolynomials: physical and combinatorial definitions

2004-11-03

arxiv.org/abs/hep-th/0411044v1

Czech.J.Phys. 54 (2004) 1223-1228

Physics

High Energy Physics

High Energy Physics - Theory

6 pages. To appear in the proceedings of the {\it XIII International Colloquium on Integrable Systems and Quantum Groups}, Cze

Scientific paper

10.1007/s10582-004-9782-2

Jack superpolynomials are eigenfunctions of the supersymmetric extension of the quantum trigonometric Calogero-Moser-Sutherland. They are orthogonal with respect to the scalar product, dubbed physical, that is naturally induced by this quantum-mechanical problem. But Jack superpolynomials can also be defined more combinatorially, starting from the multiplicative bases of symmetric superpolynomials, enforcing orthogonality with respect to a one-parameter deformation of the combinatorial scalar product. Both constructions turns out to be equivalent. This provides strong support for the correctness of the various underlying constructions and for the pivotal role of Jack superpolynomials in the theory of symmetric superpolynomials.

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