Models of q-algebra representations: q-integral transforms and ‘‘addition theorems’’

DOI10.1063/1.530581zbMath0817.17019OpenAlexW2143425720MaRDI QIDQ4300188

Ernest G. Kalnins, Willard jun. Miller

Publication date: 9 August 1994

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

Full work available at URL: https://doi.org/10.1063/1.530581

zbMATH Keywords

Mellin transform\(q\)-algebras\(q\)-deformationsrecurrence relations\(q\)-hypergeometric functionsaddition theoremEuclidean Lie algebrapseudo-Euclidean group\(q\)- integral transform identities for \(q\)-Bessel functions\(q\)-analogues of the confluent hypergeometric functions\(q\)-integral transform identitiesdiscrete integral transformintegral transform identities for \(q\)-Bessel functionsmodels of irreducible representations

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) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (8)

The quantum group of plane motions and the Hahn-Exton \(q\)-Bessel function ⋮ The quantum group of plane motions and basic Bessel functions ⋮ \(q\)-gamma and \(q\)-beta functions in quantum algebra representation theory ⋮ Yet another basic analogue of Graf's addition formula ⋮ Quantum algebra \(\varepsilon_q(2)\) and 2D \(q\)-Bessel functions ⋮ Quantum symmetries of q-difference equations ⋮ On extended umbral calculus, oscillator-like algebras and generalized Clifford algebra ⋮ \(q\)-Tricomi functions and quantum algebra representations

Cites Work

• Unitary representations of the quantum group \(\text{SU}_q(1,1)\): structure of the dual space of \({\mathcal U}_q(\mathfrak{sl}(2))\)
• Unitary representations of the quantum group \(\text{SU}_q(1,1)\). II: Matrix elements of unitary representations and the basic hypergeometric functions
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• On the quantum group and quantum algebra approach to \(q\)-special functions
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• q-analogues of the parabose and parafermi oscillators and representations of quantum algebras
• Canonical Equations and Symmetry Techniques forq-Series
• The Addition Formula for Littleq-Legendre Polynomials and the ${\operatorname{SU}}(2)$ Quantum Group
• Addition formulas for q-Bessel functions
• Models of q-algebra representations: Tensor products of special unitary and oscillator algebras
• Models of q-algebra representations: Matrix elements of the q-oscillator algebra
• A basic analogue of graf's addition formula and related formulas
• The confluent hypergeometric functions and representations of a four‐parameter lie group
• Lie Theory and q-Difference Equations
• Summations and Transformations for Basic Appell Series

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