Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/9609041,
title = {Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model},
author = {Hideaki Ujino and Miki Wadati},
journal= {arXiv preprint arXiv:cond-mat/9609041},
year = {2009}
}
Comments
17 pages, LaTeX file using jpsj.sty (ver. 0.8), cite.sty, subeqna.sty, subeqn.sty, jpsjbs1.sty and jpsjbs2.sty (all included.) You can get all the macros from ftp.u-tokyo.ac.jp/pub/SOCIETY/JPSJ/