Models of q-algebra representations: Tensor products of special unitary and oscillator algebras

DOI10.1063/1.529607zbMath0780.17014OpenAlexW2096677052MaRDI QIDQ4033943

H. L. Manocha, Willard jun. Miller, Ernest G. Kalnins

Publication date: 16 May 1993

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

Full work available at URL: https://doi.org/10.1063/1.529607

zbMATH Keywords

quantum algebrasClebsch-Gordan coefficients\(q\)-oscillator algebrabasic hypergeometric functiontensor product of representationsrealizations 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) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items

On the quantum group and quantum algebra approach to \(q\)-special functions, Quantum algebra approach to \(q\)-Gegenbauer polynomials, Models of q-algebra representations: Matrix elements of the q-oscillator algebra, Representations of the quantum algebra suq(2) on a real two-dimensional sphere, Certain inequalities for fractional \((p,q)\)-calculus, Models of q-algebra representations: q-integral transforms and ‘‘addition theorems’’, \(q\)-gamma and \(q\)-beta functions in quantum algebra representation theory, A note on tensor products of \(q\)-algebra representations and orthogonal polynomials, Yet another basic analogue of Graf's addition formula, P,Q-differentiation, P,Q-integration, and P,Q-hypergeometric functions related to quantum groups, On \(q\)-special matrix functions using quantum algebraic techniques, On irreducible \(p,q\)-representations of gl(2)., Quantum symmetries of q-difference equations, Finite Mellin transform for \((p,q)\) and symmetric calculus, Unnamed Item, Classical inequalities for \((p, q)\)-calculus on finite intervals, Classical and quantum Heisenberg groups, their representations and applications

Cites Work

• Symmetry techniques for q-series: Askey-Wilson polynomials
• Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
• 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
• On q-tensor operators for quantum groups
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Classical orthogonal polynomials of a discrete variable on nonuniform lattices
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• The q-analogue of the Laguerre polynomials
• On coherent states for the simplest quantum groups
• q-ANALOGUE OF BOSON COMMUTATOR AND THE QUANTUM GROUPS SU_q(2) AND SU_q(1, 1)
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• The quantum group SU_q(2) and a q-analogue of the boson operators
• q-analogues of the parabose and parafermi oscillators and representations of quantum algebras
• On the q oscillator and the quantum algebra su_q(1,1)
• A Note on Wilson Polynomials
• Canonical Equations and Symmetry Techniques forq-Series
• The Addition Formula for Littleq-Legendre Polynomials and the ${\operatorname{SU}}(2)$ Quantum Group
• Lie Theory and q-Difference Equations
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen