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Compatibility and companions for Leonard pairs (Q5869484)

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scientific article; zbMATH DE number 7593983

Language	Label	Description	Also known as
English	Compatibility and companions for Leonard pairs	scientific article; zbMATH DE number 7593983

Statements

scholarly article

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Nomura, Kazumasa

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Paul M. Terwilliger

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publication date

28 September 2022

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full work available at URL

https://arxiv.org/abs/2112.13326

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https://journals.uwyo.edu/index.php/ela/article/view/6861

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zbMATH Keywords

Leonard system

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parameter array

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compatibility

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companion

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bond relation

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MaRDI profile type

MaRDI publication profile

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arXiv classification

math.RA

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

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Leonard triples from Leonard pairs constructed from the standard basis of the Lie algebra

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An integrable structure related with tridiagonal algebras

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Deformed Dolan-Grady relations in quantum integrable models

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The \(q\)-deformed analogue of the Onsager algebra: beyond the Bethe ansatz approach

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A family of tridiagonal pairs and related symmetric functions

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The half-infinite XXZ chain in Onsager's approach

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A deformed analogue of Onsager’s symmetry in the XXZ open spin chain

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Exact spectrum of the XXZ open spin chain from the<i>q</i>-Onsager algebra representation theory

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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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Tridiagonal pairs of \(q\)-Racah type, the double lowering operator \({\psi}\), and the quantum algebra \(U_q(\mathfrak{sl}_2)\)

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The algebra \(U_q(\mathfrak{sl}_2)\) in disguise

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

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Spin Leonard pairs

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Some formulas for spin models on distance-regular graphs

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Distance-regular graphs

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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 universal DAHA of type (C1∨,C1) and Leonard triples

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The Rahman polynomials and the Lie algebra $\mathfrak{sl}_{3}(\mathbb{C})$

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Evaluation modules for the \(q\)-tetrahedron algebra

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

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Finite-Dimensional Irreducible Modules for the Three-Point 2 Loop Algebra

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Tridiagonal pairs of \(q\)-Racah type

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Hypergeometric Orthogonal Polynomials and Their q-Analogues

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\(Q\)-polynomial distance-regular graphs and a double affine Hecke algebra of rank one

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Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual \(q\)-Krawtchouk polynomials

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Orthogonal Polynomials, Duality and Association Schemes

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The attenuated space poset \(\mathcal{A}_q(N, M)\)

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Bipartite \(Q\)-polynomial distance-regular graphs and uniform posets

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Balanced Leonard pairs

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Affine transformations of a Leonard pair

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Krawtchouk polynomials, the Lie algebra \(\mathfrak{sl}_2\), and Leonard pairs

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The universal DAHA of type \((C_1^\vee, C_1)\) and Leonard pairs of \(q\)-Racah type

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Leonard pairs, spin models, and distance-regular graphs

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A bilinear form relating two Leonard systems

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

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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; the TD-D canonical form and the LB-UB canonical form

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Leonard pairs from 24 points of view.

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

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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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Notes on the Leonard system classification

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Dual polar graphs, the quantum algebra \(U_q(\mathfrak{sl}_{2})\), and Leonard systems of dual \(q\)-Krawtchouk type

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Identifiers

zbMATH Open document ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5869484

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