Onsager代数表示中某些Chebyshev型多项式的结构
Structure of Certain Chebyshev-type Polynomials in Onsager's Algebra Representation
摘要：
在这份报告中，我们提出了一个系统的数学结构的某些特殊的多项式所产生的能量研究的超可积$N$状态手征Potts模型的有限数量的大小。低位扇区的多项式有两种不同的表示形式，其中一种直接关系到超可积手征Potts $\ZZ_N$ -自旋链通过Onsager代数表示理论的能量描述.这两类多项式都满足某些$(N+1)$项递推关系和$N$阶微分方程;一类多项式显示某些Chebyshev类性质。本文对$N=2, 3$情形给出了严格的数学证明，并进一步对一般$N$的特殊多项式给出了一些数学证明。
英文摘要：
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 $N$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
