Onsager's algebra and partially orthogonal polynomials
High Energy Physics - Theory
2009-11-07 v1 Exactly Solvable and Integrable Systems
Abstract
The energy eigenvalues of the superintegrable chiral Potts model are determined by the zeros of special polynomials which define finite representations of Onsager's algebra. The polynomials determining the low-sector eigenvalues have been given by Baxter in 1988. In the Z_3-case they satisfy 4-term recursion relations and so cannot form orthogonal sequences. However, we show that they are closely related to Jacobi polynomials and satisfy a special "partial orthogonality" with respect to a Jacobi weight function.
Cite
@article{arxiv.hep-th/0201195,
title = {Onsager's algebra and partially orthogonal polynomials},
author = {G. von Gehlen},
journal= {arXiv preprint arXiv:hep-th/0201195},
year = {2009}
}
Comments
8 pages, no figures