Circular bidiagonal pairs

DOI10.1016/j.laa.2023.03.019zbMath1530.15007arXiv2301.00121OpenAlexW4360603747MaRDI QIDQ6046075

Arjana Žitnik, Paul M. Terwilliger

Publication date: 15 May 2023

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

Full work available at URL: https://arxiv.org/abs/2301.00121

zbMATH Keywords

tridiagonal pairLeonard pairHessenberg pairbidiagonal pair

Mathematics Subject Classification ID

Algebraic systems of matrices (15A30) Canonical forms, reductions, classification (15A21) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Diagonalization, Jordan forms (15A20)

Cites Work

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• The algebra \(U_q(\mathfrak{sl}_2)\) in disguise
• Thin Hessenberg pairs and double Vandermonde matrices
• Two commuting operators associated with a tridiagonal pair
• Bidiagonal triples
• Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials
• A classification of sharp tridiagonal pairs
• Tridiagonal pairs of \(q\)-Racah type
• Hessenberg pairs of linear transformations
• A new current algebra and the reflection equation
• Thin Hessenberg pairs
• Leonard pairs from 24 points of view.
• The shape of a tridiagonal pair.
• 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
• Notes on the Leonard system classification
• Circular Hessenberg pairs
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• Tridiagonal pairs of \(q\)-Racah type, the double lowering operator \({\psi}\), and the quantum algebra \(U_q(\mathfrak{sl}_2)\)
• A refinement of the split decomposition of a tridiagonal pair
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form
• THE AUGMENTED TRIDIAGONAL ALGEBRA
• A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or $6 - j$ Symbols
• Orthogonal Polynomials, Duality and Association Schemes
• BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂)
• Bidiagonal triads and the tetrahedron algebra
• Some q-Exponential Formulas Involving the Double Lowering Operator ψ for a Tridiagonal Pair (Research)
• MODULES OVER QUANTUM LAURENT POLYNOMIALS
• Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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