论文标题
退化Sklyanin代数，Askey-Wilson多项式和Heun操作员
Degenerate Sklyanin algebras, Askey-Wilson polynomials and Heun operators
论文作者
论文摘要
$ q $ - 差异方程，Askey-Wilson多项式的移位和连续性关系是在三维退化的Sklyanin代数$ \ MATHFRAK {SKA} _3 _3 $和$ \ MATHFRAK {SKA} _4 $的框架中施放的。结果表明，$ q $ -para racah多项式对应于Askey-Wilson多项式的非惯性截断，构成了$ \ Mathfrak {ska} _4 $的有限维表示的基础。表明，由多项式上提高条件定义的第一阶HEUN操作员被证明形成了五维矢量空间，该空间包括$ \ Mathfrak {ska} _4 $。在五个基础运营商中最普遍的二次表达，因此，它可以提高学位不超过Heun-Askey-Wilson运营商。
The $q$-difference equation, the shift and the contiguity relations of the Askey-Wilson polynomials are cast in the framework of the three and four-dimensional degenerate Sklyanin algebras $\mathfrak{ska}_3$ and $\mathfrak{ska}_4$. It is shown that the $q$-para Racah polynomials corresponding to a non-conventional truncation of the Askey-Wilson polynomials form a basis for a finite-dimensional representation of $\mathfrak{ska}_4$. The first order Heun operators defined by a degree raising condition on polynomials are shown to form a five-dimensional vector space that encompasses $\mathfrak{ska}_4$. The most general quadratic expression in the five basis operators and such that it raises degrees by no more than one is identified with the Heun-Askey-Wilson operator.
