Abstract The original Askey–Wilson algebra introduced by Zhedanov encodes the
bispectrality properties of the eponym polynomials. The name Askey–Wilson algebra is …

The algebraic structure of the rank two Racah algebra is studied in detail. We provide an
automorphism group of this algebra, which is isomorphic to the permutation group of five …

Recent results on the Racah algebra $\mathcal {R} _n $ of rank $ n-2$ are reviewed.
$\mathcal {R} _n $ is defined in terms of generators and relations and sits in the centralizer …

In this paper we give a topological interpretation and diagrammatic calculus for the rank $(n-
2) $ Askey-Wilson algebra by proving there is an explicit isomorphism with the Kauffman …

The notion of a factorized A 2-Leonard pair is introduced. It is defined as a rank 2 Leonard
pair, with actions in certain bases corresponding to the root system of the Weyl group A 2 …

Abstract The q-deformed Bannai-Ito algebra was recently constructed in the threefold tensor
product of the quantum superalgebra osp _q (1 | 2) osp q (1| 2). It turned out to be …

Abstract An operator of Heun-Askey-Wilson type is diagonalized within the framework of the
algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and …

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 …

The oscillator Racah algebra R _n (h) R n (h) is realized by the intermediate Casimir
operators arising in the multifold tensor product of the oscillator algebra h h. An embedding …

We propose a definition by generators and relations of the rank $ n-2$ Askey-Wilson
algebra $\mathfrak {aw}(n) $ for any integer $ n $, generalising the known presentation for …