Askey-Wilson polynomials and the quantum group \(SU_ q(2)\)

DOI10.3792/pjaa.66.146zbMath0707.33010OpenAlexW2087910614MaRDI QIDQ919503

Katsuhisa Mimachi, Masatoshi Noumi

Publication date: 1990

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.66.146

zbMATH Keywords

quantum groupAskey-Wilson polynomials

Mathematics Subject Classification ID

Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (15)

The quantum group of plane motions and the Hahn-Exton \(q\)-Bessel function ⋮ The quantum group of plane motions and basic Bessel functions ⋮ Algebraization of difference eigenvalue equations related to \(U_q(\text{sl}_2)\) ⋮ Pairings and actions for dynamical quantum groups ⋮ The spectral problem for the \(q\)-Knizhnik-Zamolodchikov equation and continuous \(q\)-Jacobi polynomials ⋮ Quantum group and magnetic translations Bethe ansatz for the Asbel-Hofstadter problem ⋮ Vertex-IRF transformations, dynamical quantum groups and harmonic analysis ⋮ \(q\)-Tricomi functions and quantum algebra representations ⋮ The dynamical \(U(n)\) quantum group ⋮ Quantum algebras, Kravchuk \(q\)-polynomials, and Kravchuk-Meixner \(q\)-function ⋮ The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra ⋮ Unnamed Item ⋮ Elliptic quantum group \(U_{q,p}(\widehat{\mathfrak{sl}}_2)\), Hopf algebroid structure and elliptic hypergeometric series ⋮ The q‐Bannai–Ito algebra and multivariate (−q)‐Racah and Bannai–Ito polynomials ⋮ A family of quantum projective spaces and related $q$-hypergeometric orthogonal polynomials

Cites Work

• Unnamed Item
• Quantum 2-spheres and big q-Jacobi polynomials
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Product and Addition Formulas for the Continuous q-Ultraspherical Polynomials

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