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

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dc.creatorRoan, Shi-shyr
dc.date2005-01-17
dc.date2007-04-13
dc.date.accessioned2026-07-07T07:56:25Z
dc.date.available2026-07-07T07:56:25Z
dc.descriptionIn 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 $N$.
dc.description18 pages, Latex ; Typos corrected, Small changes for clearer presentation
dc.identifierhttps://arxiv.org/abs/math-ph/0501045
dc.identifierhttp://arxiv.org/abs/math-ph/0501045
dc.identifierJournal of Computational and Applied Mathematics 202 (2007) 88-104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127301
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectExactly Solvable and Integrable Systems
dc.subject39A10; 33E30; 82B20
dc.titleStructure of Certain Chebyshev-type Polynomials in Onsager's Algebra Representation
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