Little and Big $q-$Jacobi Polynomials and the Askey-Wilson algebra

Abstract

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 ${\mathfrak{U}}_q(sl(2))$.

v2: References added. 15 pp