Weyl shift of \(q\)-oscillator and \(q\)-polynomials

DOI10.1007/BF01019333zbMath0794.33013MaRDI QIDQ1326840

Alexei Zhedanov

Publication date: 13 July 1994

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Weyl operator\(q\)-Hermite polynomials\(q\)-Charlier polynomialsWeyl \(q\)-operator

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Coherent states (81R30) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80) Other basic hypergeometric functions and integrals in several variables (33D70)

Cites Work

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• Classical orthogonal polynomials of a discrete variable and representations of the three-dimensional rotation group
• Lie algebras and recurrence relations. III: \(q\)-analogs and quantized algebras
• THE “HIGGS ALGEBRA” AS A ‘QUANTUM’ DEFORMATION OF SU(2)
• The q-deformed boson realisation of the quantum group SU(n)_qand its representations
• Nonlinear shifts of q-Bose operators and q-coherent states
• Hilbert spaces of analytic functions and generalized coherent states

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