The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey–Wilson algebra. The operators that these polynomials respectively diagonalize are identified within the Askey–Wilson algebra generated by twisted primitive elements of \(\mathfrak U_q(sl(2))\). The little q-Jacobi operator and a tridiagonalization of it are shown to realize the equitable embedding of the Askey–Wilson algebra into \(\mathfrak U_q(sl(2))\).

中文翻译：

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大和小q -Jacobi多项式和Askey-Wilson代数

q- Jacobi多项式大而小被证明是Askey-Wilson代数表示的基础向量。这些多项式分别对角化的运算符在由\（\ mathfrak U_q（sl（2））\）扭曲的原始元素生成的Askey-Wilson代数中进行标识。示出了小的q -Jacobi算符及其三对角线化实现了Askey-Wilson代数到\（\ mathfrak U_q（sl（2））\）的等价嵌入。