Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model

Details Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model

1996-09-04

arxiv.org/abs/cond-mat/9609041v1

J. Phys. Soc. Jpn. 65 (1996) 2423--2439

Physics

Condensed Matter

17 pages, LaTeX file using jpsj.sty (ver. 0.8), cite.sty, subeqna.sty, subeqn.sty, jpsjbs1.sty and jpsjbs2.sty (all included.)

Scientific paper

10.1143/JPSJ.65.2423

The Hi-Jack symmetric polynomials, which are associated with the simultaneous eigenstates for the first and second conserved operators of the quantum Calogero model, are studied. Using the algebraic properties of the Dunkl operators for the model, we derive the Rodrigues formula for the Hi-Jack symmetric polynomials. Some properties of the Hi-Jack polynomials and the relationships with the Jack symmetric polynomials and with the basis given by the QISM approach are presented. The Hi-Jack symmetric polynomials are strong candidates for the orthogonal basis of the quantum Calogero model.

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