Three mutually adjacent Leonard pairs

DOI10.1016/j.laa.2005.04.005zbMath1080.15015arXivmath/0508415OpenAlexW2049345856MaRDI QIDQ2568357

Brian Hartwig

Publication date: 10 October 2005

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

Full work available at URL: https://arxiv.org/abs/math/0508415

zbMATH Keywords

linear transformationstridiagonal formLeonard pair

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Linear transformations, semilinear transformations (15A04) Canonical forms, reductions, classification (15A21)

Related Items (23)

Matrix units associated with the split basis of a Leonard pair ⋮ Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair ⋮ Normalized Leonard pairs and Askey--Wilson relations ⋮ Compatibility and companions for Leonard pairs ⋮ The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra ⋮ Unnamed Item ⋮ A characterization of Leonard pairs using the parameters \(\{a_i\}^d_{i=0}\) ⋮ Unnamed Item ⋮ Near-bipartite Leonard pairs ⋮ Sharp tridiagonal pairs ⋮ Towards a classification of the tridiagonal pairs ⋮ A linear map acts as a Leonard pair with each of the generators of \(U(s l_2)\) ⋮ Unnamed Item ⋮ The structure of a tridiagonal pair ⋮ The switching element for a Leonard pair ⋮ BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂) ⋮ Leonard pairs having LB-TD form ⋮ The determinant of \(AA^{*} - A^{*}A\) for a Leonard pair \(A,A^{*}\) ⋮ TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS ⋮ \(p\)-inverting pairs of linear transformations and the \(q\)-tetrahedron algebra ⋮ Transition maps between the 24 bases for a Leonard pair ⋮ Tridiagonal pairs and the \(q\)-tetrahedron algebra ⋮ On the shape of a tridiagonal pair

Cites Work

• Unnamed Item
• Leonard pairs from 24 points of view.
• Leonard pairs and the \(q\)-Racah polynomials
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition
• Introduction to Leonard pairs.
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form
• TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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