The Askey–Wilson algebra and its avatars
Abstract The original Askey–Wilson algebra introduced by Zhedanov encodes the
bispectrality properties of the eponym polynomials. The name Askey–Wilson algebra is …
bispectrality properties of the eponym polynomials. The name Askey–Wilson algebra is …
The Racah algebra: an overview and recent results
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 …
$\mathcal {R} _n $ is defined in terms of generators and relations and sits in the centralizer …
Representations of the rank two Racah algebra and orthogonal multivariate polynomials
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 …
automorphism group of this algebra, which is isomorphic to the permutation group of five …
Racah Algebras, the Centralizer and Its Hilbert–Poincaré Series
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 …
025203, 2017. arXiv: 1610.02638) is recalled. A quotient of this algebra by central elements …
Algebraic (super-) integrability from commutants of subalgebras in universal enveloping algebras
R Campoamor-Stursberg, D Latini… - Journal of Physics A …, 2023 - iopscience.iop.org
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 …
universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians …
Factorized -Leonard pair
N Crampe, M Zaimi - arXiv preprint arXiv:2312.08312, 2023 - arxiv.org
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 …
pair, with actions in certain bases corresponding to the root system of the Weyl group $ A_2 …
The Higher Rank q-Deformed Bannai-Ito and Askey-Wilson Algebra
H De Bie, H De Clercq, W van de Vijver - … in Mathematical Physics, 2020 - Springer
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 …
product of the quantum superalgebra osp _q (1 | 2) osp q (1| 2). It turned out to be …
The generalized Racah algebra as a commutant
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 …
{$\mathfrak {o}(2)^{\oplus n} $} subalgebra of $\mathfrak {o}(2n) $ in oscillator …
Finite-dimensional irreducible modules of the Racah algebra at characteristic zero
HW Huang, S Bockting-Conrad - SIGMA. Symmetry, Integrability and …, 2020 - emis.de
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 …
The Racah algebra $\Re $ is the unital associative ${\mathbb F} $-algebra defined by …
-Griffiths polynomials: Bispectrality and biorthogonality
We introduce a generalization of bivariate Griffiths polynomials depending on an additional
parameter $\lambda $. These $\lambda $-Griffiths polynomials are bivariate, bispectral and …
parameter $\lambda $. These $\lambda $-Griffiths polynomials are bivariate, bispectral and …