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

DOI10.1080/03081087.2012.753597zbMath1322.17005OpenAlexW2043035654MaRDI QIDQ2872531

Hasan Alnajjar, Curtin, Brian

Publication date: 15 January 2014

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

Full work available at URL: https://doi.org/10.1080/03081087.2012.753597

zbMATH Keywords

Leonard pairsfinite-dimensional \(sl_2\)-modulesstandard eigenbases

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 (5)

Bidiagonal triads and the tetrahedron algebra ⋮ Unnamed Item ⋮ A linear map acts as a Leonard pair with each of the generators of \(U(s l_2)\) ⋮ Lowering-raising triples and \(U_q(\mathfrak{sl}_2)\) ⋮ A tridiagonal linear map with respect to eigenbases of equitable basis ofsl₂

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
• 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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