Representations of the quantum algebra suq(2) on a real two-dimensional sphere

DOI10.1063/1.530248zbMath0792.17013OpenAlexW2035159563MaRDI QIDQ4276816

Pavel Winternitz, Guy Rideau

Publication date: 19 April 1994

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

Full work available at URL: https://doi.org/10.1063/1.530248

zbMATH Keywords

irreducible representationsquantum group \(\text{SU}_ q(2)\)\(q\)- special functions\(q\)-Vilenkin functions

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (6)

A Rodriguez formula and integration measure for the quantum deformed Legendre functions ⋮ The q-Coulomb problem in configuration space ⋮ Schrödinger equations for \(\text{su}_ q(2)\)-invariant quantum systems ⋮ Unitary representations of the quantum algebra suq(2) on a real two-dimensional sphere for q∈R+ or generic q∈S1 ⋮ Approach of spherical harmonics to the representation of the deformed su(1,1) algebra ⋮ Nonlinear differential-difference and difference equations: integrability and exact solvability

Cites Work

• Unitary representations of the quantum group \(\text{SU}_q(1,1)\): structure of the dual space of \({\mathcal U}_q(\mathfrak{sl}(2))\)
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Compact matrix pseudogroups
• Quantum spheres
• Poisson manifolds and the Schouten bracket
• Big \(q\)-Jacobi polynomials, \(q\)-Hahn polynomials, and a family of quantum 3-spheres
• q-analogues of the parabose and parafermi oscillators and representations of quantum algebras
• The Addition Formula for Littleq-Legendre Polynomials and the ${\operatorname{SU}}(2)$ Quantum Group
• The metaplectic representation of suq(1,1) and the q-Gegenbauer polynomials
• Models of q-algebra representations: Tensor products of special unitary and oscillator algebras
• A new basis for the representations of the rotation group. Lamé and Heun polynomials

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