The algebra of dual −1 Hahn polynomials and the Clebsch-Gordan problem of sl−1(2)

DOI10.1063/1.4790417zbMath1280.81071arXiv1207.4220OpenAlexW2034541598MaRDI QIDQ5396287

Alexei Zhedanov, Luc Vinet, Vincent X. Genest

Publication date: 5 February 2014

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

Full work available at URL: https://arxiv.org/abs/1207.4220

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 functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Hopf algebras and their applications (16T05)

Related Items (7)

A representation of the Dunkl oscillator model on curved spaces: Factorization approach ⋮ Doubling (dual) Hahn polynomials: classification and applications ⋮ A Howe correspondence for the algebra of the \(\mathfrak{osp}(1 | 2)\) Clebsch-Gordan coefficients ⋮ The Dunkl oscillator in the plane. II: Representations of the symmetry algebra ⋮ A Laplace-Dunkl equation on \(S^2\) and the Bannai-Ito algebra ⋮ Convolution identities for Dunkl orthogonal polynomials from the osp(1|2) Lie superalgebra ⋮ Perfect state transfer in a spin chain without mirror symmetry

Cites Work

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• A Bochner theorem for Dunkl polynomials
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• Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan–Schwinger map
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• Jordan algebras and orthogonal polynomials
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• Hypergeometric Orthogonal Polynomials and Their q-Analogues
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• Two linear transformations each tridiagonal with respect to an eigenbasis of the other
• Unnamed Item

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