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 …

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 …

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 …

Starting from a purely algebraic procedure based on the commutant of a subalgebra in the
universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians …

The notion of 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 …

The Racah algebra $ R (n) $ of rank $(n-2) $ is obtained as the commutant of the\mbox
{$\mathfrak {o}(2)^{\oplus n} $} subalgebra of $\mathfrak {o}(2n) $ in oscillator …

Abstract Assume that ${\mathbb F} $ is an algebraically closed field with characteristic zero.
The Racah algebra $\Re $ is the unital associative ${\mathbb F} $-algebra defined by …

We introduce a generalization of bivariate Griffiths polynomials depending on an additional
parameter $\lambda $. These $\lambda $-Griffiths polynomials are bivariate, bispectral and …