论文标题
第2等级的Askey-Wilson代数
An Askey-Wilson Algebra of Rank 2
论文作者
论文摘要
引入了一个代数，该代数可被视为Askey-Wilson代数的等级2扩展。该代数中的关系是由在量子代数$ \ mathcal {u} _ {q}（\ mathfrak {slfrak {sl}（2，\ mathbb c）的量子代数;结果表明，双变量$ q $ -racah多项式似乎是代数发电机特征向量的重叠系数。此外，使用代数的定义关系计算相应的$ q $差异运算符，表明它编码了双变量$ q $ -racah多项式的双光谱属性。
An algebra is introduced which can be considered as a rank 2 extension of the Askey-Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the quantum algebra $\mathcal{U}_{q}(\mathfrak{sl}(2,\mathbb C))$. It is shown that bivariate $q$-Racah polynomials appear as overlap coefficients of eigenvectors of generators of the algebra. Furthermore, the corresponding $q$-difference operators are calculated using the defining relations of the algebra, showing that it encodes the bispectral properties of the bivariate $q$-Racah polynomials.
