Coupling coefficients of \(\operatorname{su}_{q}(1,1)\) and multivariate \(q\)-Racah polynomials

DOI10.1016/j.nuclphysb.2017.12.009zbMath1380.81166arXiv1702.04626OpenAlexW2590077165MaRDI QIDQ1701133

Vincent X. Genest, Luc Vinet, Plamen Iliev

Publication date: 22 February 2018

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.04626

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) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Groups and algebras in quantum theory and relations with integrable systems (81R12) Quantum groups (quantized function algebras) and their representations (20G42)

Related Items (4)

\(3nj\)-symbols and identities for \(q\)-Bessel functions ⋮ An Askey-Wilson algebra of rank 2 ⋮ The higher rank \(q\)-deformed Bannai-Ito and Askey-Wilson algebra ⋮ The q‐Bannai–Ito algebra and multivariate (−q)‐Racah and Bannai–Ito polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The quantum superalgebra \(\mathfrak{osp}_q(1| 2)\) and a \(q\)-generalization of the Bannai-Ito polynomials
• The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
• Superintegrability in two dimensions and the Racah-Wilson algebra
• Connection coefficients for classical orthogonal polynomials of several variables
• Multivariable Askey-Wilson function and bispectrality
• The tree method for multidimensional \(q\)-Hahn and \(q\)-Racah polynomials
• Gaudin models with \(\mathcal U_q(\mathfrak{osp}(1|2))\) symmetry
• Discrete orthogonal polynomials and difference equations of several variables
• Racah polynomials and recoupling schemes of \(\mathfrak{su}(1,1)\)
• Bispectrality of multivariable Racah-Wilson polynomials
• ``Hidden symmetry of Askey-Wilson polynomials
• Clebsch-Gordan coefficients for \({\mathcal U}_ q({\text{su}}(1,1))\) and \({\mathcal U}_ q({\text{sl}}(2))\), and linearization formula of matrix elements
• Multivariable \(q\)-Hahn polynomials as coupling coefficients for quantum algebra representations
• The generic quantum superintegrable system on the sphere and Racah operators
• Multivariable \(q\)-Racah polynomials
• Embeddings of the Racah algebra into the Bannai-Itô algebra
• Some systems of multivariable orthogonal \(q\)-Racah polynomials
• Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials
• Exact solution of the quantum Calogero–Gaudin system and of its q deformation
• Classical and quantum superintegrability with applications
• The multivariate Hahn polynomials and the singular oscillator
• Bispectral commuting difference operators for multivariable Askey-Wilson polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Orthogonal Polynomials in Two Variables of q-Hahn and q-Jacobi Type
• Some multivariable orthogonal polynomials of the Askey tableau—Continuous families
• Some multivariable orthogonal polynomials of the Askey tableau-discrete families
• Multivariable Orthogonal Polynomials and Coupling Coefficients for Discrete Series Representations
• Convolutions for Orthogonal Polynomials from Lie and Quantum Algebra Representations
• The Bannai-Ito polynomials as Racah coefficients of the $sl_{-1}(2)$ algebra
• Orthogonal Polynomials of Several Variables

This page was built for publication: Coupling coefficients of \(\operatorname{su}_{q}(1,1)\) and multivariate \(q\)-Racah polynomials