Bannai-Ito algebras and the universal \(R\)-matrix of \(\mathfrak{osp}(1\!\!\mid\!\!2)\)

DOI10.1007/s11005-019-01249-wzbMath1472.16030arXiv1909.06426OpenAlexW3111277666MaRDI QIDQ1987169

Meri Zaimi, Luc Vinet, Nicolas Crampé

Publication date: 9 April 2020

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.06426

zbMATH Keywords

centralizeruniversal \(R\)-matrixBannai-Ito algebra

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Applications of Lie (super)algebras to physics, etc. (17B81) Ring-theoretic aspects of quantum groups (16T20)

Related Items (5)

Askey-Wilson braid algebra and centralizer of \(U_q (\mathfrak{sl}_2)\) ⋮ Racah problems for the oscillator algebra, the Lie algebra \(\mathfrak{sl}_n\), and multivariate Krawtchouk polynomials ⋮ Temperley-Lieb, Birman-Murakami-Wenzl and Askey-Wilson algebras and other centralizers of \(U_q(\mathfrak{sl}_2)\) ⋮ Braid group and 𝑞-Racah polynomials ⋮ The Askey–Wilson algebra and its avatars

Cites Work

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• A Dirac-Dunkl equation on \(S^2\) and the Bannai-Ito algebra
• The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
• Dunkl shift operators and Bannai-Ito polynomials
• The enveloping algebra of the Lie superalgebra \(\mathfrak{osp}(1,2)\)
• The higher rank \(q\)-deformed Bannai-Ito and Askey-Wilson algebra
• A remark on the Casimir elements of Lie superalgebras and quantized Lie superalgebras
• 𝔬𝔰𝔭(1,2) and generalized Bannai–Ito algebras
• The Bannai-Ito polynomials as Racah coefficients of the $sl_{-1}(2)$ algebra
• Revisiting the Askey–Wilson algebra with the universal R-matrix of $\boldsymbol{ \newcommand{\su}{\mathfrak{sl}} U_q(\su_2)}$
• Lie superalgebras

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