New realizations of algebras of the Askey–Wilson type in terms of Lie and quantum algebras

DOI10.1142/S0129055X21500021zbMath1486.33019arXiv2005.06957WikidataQ115213267 ScholiaQ115213267MaRDI QIDQ5156032

Nicolas Crampé, Dounia Shaaban Kabakibo, Luc Vinet

Publication date: 14 October 2021

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

Full work available at URL: https://arxiv.org/abs/2005.06957

zbMATH Keywords

orthogonal polynomialsLie algebrasAskey-Wilson algebra

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) Connections of hypergeometric functions with groups and algebras, and related topics (33C80)

Related Items (5)

Racah algebras, the centralizer \(Z_n(\mathfrak{sl}_2)\) and its Hilbert-Poincaré series ⋮ Matrix elements of SO(3) in sl3 representations as bispectral multivariate functions ⋮ Bethe ansatz diagonalization of the Heun-Racah operator ⋮ Representations of the rank two Racah algebra and orthogonal multivariate polynomials ⋮ The Askey–Wilson algebra and its avatars

Cites Work

• Superintegrability in two dimensions and the Racah-Wilson algebra
• The universal Askey-Wilson algebra and the equitable presentation of \(U_{q}(sl_{2})\)
• The Higgs and Hahn algebras from a Howe duality perspective
• Normalized Leonard pairs and Askey--Wilson relations
• Deformed Dolan-Grady relations in quantum integrable models
• ``Hidden symmetry of Askey-Wilson polynomials
• Algebraic Heun operator and band-time limiting
• Superintegrable systems: Polynomial algebras and quasi-exactly solvable Hamiltonians
• Little and big \(q\)-Jacobi polynomials and the Askey-Wilson algebra
• Askey-Wilson relations and Leonard pairs
• The quantum algebra \(U_q(\mathfrak{sl}_2)\) and its equitable presentation
• THE “HIGGS ALGEBRA” AS A ‘QUANTUM’ DEFORMATION OF SU(2)
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Convolutions for Orthogonal Polynomials from Lie and Quantum Algebra Representations
• Bigq-Laguerre andq-Meixner polynomials and representations of the quantum algebraU_q(su_1,1)
• Linear covariance algebra for SL_q(2)
• Truncation of the reflection algebra and the Hahn algebra
• Askey–Wilson Polynomials as Zonal Spherical Functions on the ${\operatorname{SU}}(2)$ Quantum Group

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