Finite-dimensional irreducible modules of the universal Askey-Wilson algebra

Understand

Since the introduction of Askey-Wilson algebras by Zhedanov in 1991, the classification of the finite-dimensional irreducible modules of Askey-Wilson algebras remains open.

• A universal analog $\triangle_q$ of the Askey-Wilson algebras was recently studied.
• In this paper, we consider a family of infinite-dimensional $\triangle_q$-modules.
• By the universal property of these $\triangle_q$-modules, we classify the finite-dimensional irreducible $\triangle_q$-modules when $q$ is not a root of unity.