New commutation and q-commutation relations are proven for generators of the higher rank Askey-Wilson and q-Bannai-Ito algebras, extending the rank-one defining relations.
Finite-dimensional irreducible modules of the universal Askey-Wilson algebra
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abstract
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.
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Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra
New commutation and q-commutation relations are proven for generators of the higher rank Askey-Wilson and q-Bannai-Ito algebras, extending the rank-one defining relations.