Tridiagonal pairs, alternating elements, and distance-regular graphs

DOI10.1016/J.JCTA.2022.105724OpenAlexW4313568674MaRDI QIDQ2689004

Paul M. Terwilliger

Publication date: 6 March 2023

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.07741

zbMATH Keywords

distance-regular graphtridiagonal pair\(q\)-Serre relationsalternating elements

Mathematics Subject Classification ID

Groups and algebras in quantum theory (81Rxx) Lie algebras and Lie superalgebras (17Bxx) Algebraic combinatorics (05Exx)

Cites Work

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• Distance-regular graphs
• A classification of sharp tridiagonal pairs
• The subconstituent algebra of an association scheme. I
• Deformed Dolan-Grady relations in quantum integrable models
• A new (in)finite-dimensional algebra for quantum integrable models
• A bilinear form for tridiagonal pairs of \(q\)-Serre type
• Sharp tridiagonal pairs
• Towards a classification of the tridiagonal pairs
• A new current algebra and the reflection equation
• Distance-regular graphs and the \(q\)-tetrahedron algebra
• Quantum affine algebras
• Quantum groups and quantum shuffles
• A basis of type Poincaré-Birkhoff-Witt for the quantum algebra of \(\widehat{sl}(2)\)
• Braid group action and quantum affine algebras
• The shape of a tridiagonal pair.
• Tight distance-regular graphs and the subconstituent algebra
• A family of tridiagonal pairs
• On the second realization for the positive part of \(U_q (\widehat{sl_2})\) of equitable type
• Using Catalan words and a \(q\)-shuffle algebra to describe the Beck PBW basis for the positive part of \(U_q( \widehat{\mathfrak{sl}}_2)\)
• Tridiagonal pairs of \(q\)-Serre type and their linear perturbations
• The alternating central extension for the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\)
• Algebraic combinatorics. Translated from the Japanese
• The alternating presentation of \(U_q(\widehat{gl_2})\) from Freidel-Maillet algebras
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• Evaluation modules for the \(q\)-tetrahedron algebra
• TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
• THE AUGMENTED TRIDIAGONAL ALGEBRA
• TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS
• A family of tridiagonal pairs related to the quantum affine algebra U_q(sl_2)
• A compact presentation for the alternating central extension of the positive part of Uq(sl^2)
• The alternating PBW basis for the positive part of Uq(sl^2)
• Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules
• Introduction to quantum groups
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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