Onsager's algebra and partially orthogonal polynomials

Details Onsager's algebra and partially orthogonal polynomials Onsager's algebra and partially orthogonal polynomials

2002-01-24

arxiv.org/abs/hep-th/0201195v1

Int.J.Mod.Phys. B16 (2002) 2129-2136

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, no figures

Scientific paper

10.1142/S0217979202011883

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.

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