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Structure of Certain Chebyshev-type Polynomials in Onsager's Algebra Representation

Shi-shyr Roan
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Abstract

In this report, we present a systematic account of mathematical structures of certain special polynomials arisen from the energy study of the superintegrable $N$-state chiral Potts model with a finite number of sizes. The polynomials of low-lying sectors are represented in two different forms, one of which is directly related to the energy description of superintegrable chiral Potts $\ZZ_N$-spin chain via the representation theory of Onsager's algebra. Both two types of polynomials satisfy some $(N+1)$-term recurrence relations, and $N$th order differential equations; polynomials of one kind reveal certain Chebyshev-like properties. Here we provide a rigorous mathematical argument for cases $N=2, 3$, and further raise some mathematical conjectures on those special polynomials for a general $N$.

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BibTeXRIS

Shi-shyr Roan. 2007-04-13. Structure of Certain Chebyshev-type Polynomials in Onsager's Algebra Representation. https://arxiv.org/abs/math-ph/0501045

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