Leonard triples from the equitable basis of \(sl_2\)

DOI10.1016/j.laa.2015.05.018zbMath1394.17015OpenAlexW308993672MaRDI QIDQ492769

Hasan Alnajjar, Curtin, Brian

Publication date: 21 August 2015

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

Full work available at URL: https://doi.org/10.1016/j.laa.2015.05.018

zbMATH Keywords

Krawtchouk typeRacah typeHahn typeLeonard pairs

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Association schemes, strongly regular graphs (05E30)

Related Items (2)

Unnamed Item ⋮ Leonard triples of \(q\)-Racah type and their pseudo intertwiners

Cites Work

• The universal Askey-Wilson algebra
• Leonard triples from Leonard pairs constructed from the standard basis of the Lie algebra
• The equitable basis for \({\mathfrak{sl}_2}\)
• Double affine Hecke algebras of rank 1 and the \(\mathbb Z_3\)-symmetric Askey-Wilson relations
• The classification of Leonard triples of QRacah type
• The subconstituent algebra of an association scheme. III
• Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair
• The tetrahedron algebra and its finite-dimensional irreducible modules
• The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra
• Modular Leonard triples
• Leonard triples and hypercubes
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array
• Introduction to Leonard pairs.
• Spin Leonard pairs
• The classification of Leonard triples that have Bannai/Ito type and odd diameter
• The classification of Leonard triples of Racah type
• Totally bipartite Leonard pairs and totally bipartite Leonard triples of \(q\)-Racah type
• The universal Askey-Wilson algebra and DAHA of type \((C_{1}^{\vee },C_{1})\)
• Leonard Pairs and Leonard Triples ofq-Racah Type from the Quantum AlgebraU_q(sl₂)
• The Leonard triples extended from given Leonard pairs of Bannai/Ito type
• Leonard pairs from the equitable basis of sl2
• Orthogonal Polynomials, Duality and Association Schemes
• LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
• Finite-Dimensional Irreducible Modules for the Three-Point 2 Loop Algebra
• Totally bipartite/abipartite Leonard pairs and Leonard triples of Bannai/ito type
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other
• Unnamed Item
• Unnamed Item

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