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Sharp tridiagonal pairs (Q927753)

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Language	Label	Description	Also known as
English	Sharp tridiagonal pairs	scientific article

Statements

scholarly article

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Sharp tridiagonal pairs (English)

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Linear Algebra and its Applications

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publication date

9 June 2008

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full work available at URL

https://arxiv.org/abs/0712.3665

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zbMATH Keywords

Leonard pair

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tridiagonal pair

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\(q\)-Racah polynomial

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orthogonal polynomial

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Nomura, Kazumasa

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Paul M. Terwilliger

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MaRDI profile type

MaRDI publication profile

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A family of tridiagonal pairs

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A family of tridiagonal pairs related to the quantum affine algebra U_q(sl_2)

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A bilinear form for tridiagonal pairs of \(q\)-Serre type

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A family of tridiagonal pairs and related symmetric functions

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Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak {\widehat{sl}_2})\) and its Borel subalgebra

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The universal central extension of the three-point $\mathfrak {sl}_2$ loop algebra

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Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak g)\) and its Borel subalgebra \(U_{q}(\mathfrak g)^{\geqslant 0}\)

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The Terwilliger algebras of bipartite \(P\)- and \(Q\)-polynomial schemes

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The Terwilliger algebra of an almost-bipartite \(P\)- and \(Q\)-polynomial association scheme

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The Terwilliger algebra of a distance-regular graph that supports a spin model

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Modular Leonard triples

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Spin Leonard pairs

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A generalization of the Terwilliger algebra

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Raising/Lowering Maps and Modules for the Quantum Affine Algebra

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Three mutually adjacent Leonard pairs

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The tetrahedron algebra and its finite-dimensional irreducible modules

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The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra

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The shape of a tridiagonal pair.

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Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).

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TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS

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The<i>q</i>-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules

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\(p\)-inverting pairs of linear transformations and the \(q\)-tetrahedron algebra

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Distance-regular graphs and the \(q\)-tetrahedron algebra

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Tridiagonal pairs of Krawtchouk type

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THE AUGMENTED TRIDIAGONAL ALGEBRA

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The quantum algebra \(U_q(\mathfrak{sl}_2)\) and its equitable presentation

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Orthogonal Polynomials, Duality and Association Schemes

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On bipartite \(Q\)-polynomial distance-regular graphs

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Leonard triples and hypercubes

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Tridiagonal pairs and the Askey--Wilson relations

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A refinement of the split decomposition of a tridiagonal pair

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Tridiagonal pairs of height one

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Balanced Leonard pairs

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Some trace formulae involving the split sequences of a Leonard pair

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The determinant of \(AA^{*} - A^{*}A\) for a Leonard pair \(A,A^{*}\)

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Matrix units associated with the split basis of a Leonard pair

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Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair

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The switching element for a Leonard pair

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Affine transformations of a Leonard pair

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The split decomposition of a tridiagonal pair

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Transition maps between the 24 bases for a Leonard pair

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On the multiplicities of the primitive idempotents of a \(Q\)-polynomial distance-regular graph

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Multivariable Orthogonal Polynomials and Coupling Coefficients for Discrete Series Representations

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An elementary approach to \(6j\)-symbols (classical, quantum, rational, trigonometric, and elliptic)

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On strongly closed subgraphs with diameter two and the \(Q\)-polynomial property

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The subconstituent algebra of an association scheme. I

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The subconstituent algebra of an association scheme. III

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Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS

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Leonard pairs from 24 points of view.

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Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form

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Introduction to Leonard pairs.

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Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition

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Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array

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Leonard pairs and the \(q\)-Racah polynomials

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The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra

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LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS

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Normalized Leonard pairs and Askey--Wilson relations

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Identifiers

zbMATH Open document ID

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10.1016/j.laa.2008.02.006

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:927753

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