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 …
A higher rank Racah algebra and the Laplace–Dunkl operator
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 …
algebra of the Laplace–Dunkl operator associated to the $\mathbb {Z} _2^ n $ root system …
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 …
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 …
On the algebra of symmetries of Laplace and Dirac operators
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 …
Dunkl operator defined in terms of the differential-difference operators associated with finite …
Racah Problems for the Oscillator Algebra, the Lie Algebra , and Multivariate Krawtchouk Polynomials
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 …
operators arising in the multifold tensor product of the oscillator algebra h h. An embedding …
Revisiting the Askey–Wilson algebra with the universal R-matrix of
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 …
terms of the universal R-matrix of. The generators of the centralizer of in its three-fold tensor …
[HTML][HTML] The Higgs and Hahn algebras from a Howe duality perspective
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 …
polynomials. In the discrete case, it is isomorphic to the polynomial algebra identified by …
[HTML][HTML] The centre of the Dunkl total angular momentum algebra
K Calvert, M De Martino, R Oste - Journal of Algebra, 2024 - Elsevier
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 …
rational Cherednik algebra H t, c (V, W) associated with (V, W) at the parameters t≠ 0 and c …