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

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 …

A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry
algebra of the Laplace–Dunkl operator associated to the $\mathbb {Z} _2^ n $ root system …

The higher rank Racah algebra R (n) introduced in De Bie et al.(J Phys A Math Theor 51 (2):
025203, 2017. arXiv: 1610.02638) is recalled. A quotient of this algebra by central elements …

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 …

We consider a generalization of the classical Laplace operator, which includes the Laplace–
Dunkl operator defined in terms of the differential-difference operators associated with finite …

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 …

A description of the embedding of a centrally extended Askey–Wilson algebra,, in is given in
terms of the universal R-matrix of. The generators of the centralizer of in its three-fold tensor …

The Hahn algebra encodes the bispectral properties of the eponymous orthogonal
polynomials. In the discrete case, it is isomorphic to the polynomial algebra identified by …

For a finite dimensional representation V of a finite reflection group W, we consider the
rational Cherednik algebra H t, c (V, W) associated with (V, W) at the parameters t≠ 0 and c …