A tridiagonal linear map with respect to eigenbases of equitable basis ofsl2

DOI10.1080/03081087.2014.947692zbMath1322.17004OpenAlexW1998982241MaRDI QIDQ4981973

Hasan Alnajjar

Publication date: 23 March 2015

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

Full work available at URL: https://doi.org/10.1080/03081087.2014.947692

zbMATH Keywords

Leonard pairsstandard eigenbasesfinite-dimensional \(sl_{2}\)-modules

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Special matrices (15B99)

Related Items (1)

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Cites Work

• The equitable basis for \({\mathfrak{sl}_2}\)
• The subconstituent algebra of an association scheme. III
• The tetrahedron algebra and its finite-dimensional irreducible modules
• The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array
• Introduction to Leonard pairs.
• A bidiagonal and tridiagonal linear map with respect to eigenbases of equitable basis ofsl₂
• Leonard pairs associated with the equitable generators of the quantum algebraU_q(sl₂)
• LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
• Finite-Dimensional Irreducible Modules for the Three-Point 2 Loop Algebra
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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