A method to derive explicit formulas for an elliptic generalization of the Jack polynomials
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
We review a method providing explicit formulas for the Jack polynomials. Our method is based on the relation of the Jack polynomials to the eigenfunctions of a well-known exactly solvable quantum many-body system of Calogero-Sutherland type. We also sketch a generalization of our method allowing to find the exact solution of the elliptic generalization of the Calogero-Sutherland model. We present the resulting explicit formulas for certain symmetric functions generalizing the Jack polynomials to the elliptic case.
Cite
@article{arxiv.math-ph/0511015,
title = {A method to derive explicit formulas for an elliptic generalization of the Jack polynomials},
author = {Edwin Langmann},
journal= {arXiv preprint arXiv:math-ph/0511015},
year = {2007}
}
Comments
14 pages, to appear in the proceedings of a workshop on "Jack, Hall-Littlewood and Macdonald polynomials", V.B. Kuznetsov and S. Sahi (eds.), Contemporary Mathematics, AMS