Leonard pairs and quantum algebra \(U_q(sl_{2})\)

DOI10.1016/J.LAA.2016.08.034zbMath1403.17021OpenAlexW2508331568MaRDI QIDQ501251

Man Sang, Bo Hou, Suo-gang Gao

Publication date: 29 December 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2016.08.034

zbMATH Keywords

quantum algebraLeonard pairequitable generatorLB-TD pair

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Association schemes, strongly regular graphs (05E30) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items (4)

A linear map acts as a Leonard pair with each of the generators of \(U(s l_2)\) ⋮ Unnamed Item ⋮ The equitable presentation for the quantum group νq(sl2) ⋮ Freidel-Maillet type presentations of \(U_q(sl_2)\)

Cites Work

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• Krawtchouk polynomials, the Lie algebra \(\mathfrak{sl}_2\), and Leonard pairs
• The equitable basis for \({\mathfrak{sl}_2}\)
• Introduction to Leonard pairs.
• Leonard pairs having LB-TD form
• The quantum algebra \(U_q(\mathfrak{sl}_2)\) and its equitable presentation
• Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view
• Leonard pairs from the equitable basis of sl2
• Leonard pairs associated with the equitable generators of the quantum algebraU_q(sl₂)
• LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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