Revisiting the Askey–Wilson algebra with the universal R-matrix of $\boldsymbol{ \newcommand{\su}{\mathfrak{sl}} U_q(\su_2)}$

DOI10.1088/1751-8121/ab604eOpenAlexW2967519741MaRDI QIDQ5870385

Nicolas Crampé, Julien Gaboriaud, Meri Zaimi, Luc Vinet

Publication date: 9 January 2023

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.04806

zbMATH Keywords

quantum groupuniversal \(R\)-matrixAskey-Wilson algebra

Mathematics Subject Classification ID

Quantum theory (81-XX) Statistical mechanics, structure of matter (82-XX)

Related Items (9)

Chern-Simons theory, link invariants and the Askey-Wilson algebra ⋮ Askey-Wilson braid algebra and centralizer of \(U_q (\mathfrak{sl}_2)\) ⋮ An Askey-Wilson algebra of rank 2 ⋮ A Howe correspondence for the algebra of the \(\mathfrak{osp}(1 | 2)\) Clebsch-Gordan coefficients ⋮ Temperley-Lieb, Birman-Murakami-Wenzl and Askey-Wilson algebras and other centralizers of \(U_q(\mathfrak{sl}_2)\) ⋮ Bannai-Ito algebras and the universal \(R\)-matrix of \(\mathfrak{osp}(1\!\!\mid\!\!2)\) ⋮ Higher rank relations for the Askey-Wilson and \(q\)-Bannai-Ito algebra ⋮ Braid group and 𝑞-Racah polynomials ⋮ The Askey–Wilson algebra and its avatars

Cites Work

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• The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
• Superintegrability in two dimensions and the Racah-Wilson algebra
• The universal Askey-Wilson algebra
• Dunkl shift operators and Bannai-Ito polynomials
• Zhedanov's algebra \(AW(3)\) and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra
• ``Hidden symmetry of Askey-Wilson polynomials
• Higher rank relations for the Askey-Wilson and \(q\)-Bannai-Ito algebra
• The higher rank \(q\)-deformed Bannai-Ito and Askey-Wilson algebra
• An embedding of the universal Askey-Wilson algebra into \(\operatorname{U}_q(\mathfrak{sl}_2) \otimes U_q(\mathfrak{sl}_2) \otimes U_q(\mathfrak{sl}_2)\)
• The relationship between Zhedanov's algebra \(AW(3)\) and the double affine Hecke algebra in the rank one case
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Temperley–Lieb, Brauer and Racah algebras and other centralizers of 𝔰𝔲(2)
• Centralizers of the superalgebra $\mathfrak{osp}(1|2)$ : the Brauer algebra as a quotient of the Bannai–Ito algebra

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