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

DOI10.1016/j.laa.2007.12.015zbMath1194.05166OpenAlexW2017314091MaRDI QIDQ924341

Hasan Alnajjar, Curtin, Brian

Publication date: 15 May 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2007.12.015

zbMATH Keywords

quantum groupbilinear formtridiagonal pair\(q\)-Serre relations

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Association schemes, strongly regular graphs (05E30) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Quadratic and bilinear forms, inner products (15A63)

Related Items (13)

Using a q-shuffle algebra to describe the basic module V(Λ_0) for the quantized enveloping algebra Uq(sl^2) ⋮ Unnamed Item ⋮ Tridiagonal pairs, alternating elements, and distance-regular graphs ⋮ Sharp tridiagonal pairs ⋮ Towards a classification of the tridiagonal pairs ⋮ Tridiagonal pairs of Krawtchouk type ⋮ The structure of a tridiagonal pair ⋮ Tridiagonal pairs and the \(\mu \)-conjecture ⋮ BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂) ⋮ A classification of sharp tridiagonal pairs ⋮ Transition maps between the 24 bases for a Leonard pair ⋮ Tridiagonal pairs and the \(q\)-tetrahedron algebra ⋮ On the shape of a tridiagonal pair

Cites Work

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• Quantum affine algebras
• The structure of nonthin irreducible \(T\)-modules of endpoint 1: Ladder bases and classical parameters
• Leonard pairs from 24 points of view.
• The shape of a tridiagonal pair.
• Introduction to Leonard pairs.
• A family of tridiagonal pairs
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• Tridiagonal pairs of Krawtchouk type
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form
• TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
• 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)
• Finite-Dimensional Irreducible Modules for the Three-Point 2 Loop Algebra
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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