A $q$-Hankel transform associated to the quantum linking groupoid for the quantum $SU(2)$ and $E(2)$ groups

DOI10.1090/S0002-9939-2015-12445-8zbMath1326.33025arXiv1308.2859MaRDI QIDQ5246879

Kenny De Commer, H. T. Koelink

Publication date: 22 April 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.2859

zbMATH Keywords

orthogonal polynomialshypergeometric functionsquantum groupscategory theory\(q\)-deformation

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Quantizations, deformations for selfadjoint operator algebras (46L65) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

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Cites Work

• On a correspondence between \(SU_q(2)\), \(\widetilde{E}_q(2)\) and \(\widetilde{SU}_q(1,1)\)
• On a Morita equivalence between the duals of quantum \(SU(2)\) and quantum \(\widetilde E(2)\)
• Quantum spheres
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Quantum \(E(2)\) group and its Pontryagin dual
• Quantum \(SU(2)\) and \(E(2)\) groups. Contraction procedure
• An explicit description of the fundamental unitary for \(SU(2)_ q\)
• The quantum group of plane motions and the Hahn-Exton \(q\)-Bessel function
• On a Hankel transform integral containing an exponential function and two Laguerre polynomials
• An invitation to quantum groups and duality. From Hopf algebras to multiplicative unitaries and beyond
• A Simple Proof of Koornwinder's Addition Formula for the Little q-Legendre Polynomials
• The Addition Formula for Littleq-Legendre Polynomials and the ${\operatorname{SU}}(2)$ Quantum Group
• On q-Analogues of the Fourier and Hankel Transforms
• Askey–Wilson Polynomials as Zonal Spherical Functions on the ${\operatorname{SU}}(2)$ Quantum Group
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