Three mutually adjacent Leonard pairs
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Publication:2568357
DOI10.1016/j.laa.2005.04.005zbMath1080.15015arXivmath/0508415OpenAlexW2049345856MaRDI QIDQ2568357
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
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 Uq(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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