A family of tridiagonal pairs
type: Item
instance of: scholarly article
title: A family of tridiagonal pairs
zbMATH Open document ID: 1060.15006
author: Hasan Alnajjar
author: Brian Curtin
published in: Linear Algebra and its Applications
publication date: 2004-11-18T00:00:00Z
review text: Let \(V\) be a vector space of finite dimension over a field, and let \(A, A^*\) be a tridiagonal pair on \(V\) of diameter at least 3, whose eigenvalue and dual eigenvalue sequences, not all having multiplicity one, satisfy certain conditions. Given \(V = Mv^* + M^*v\), where \(M\) and \(M^*\) are the subalgebras of End\((V)\) generated by \(A, A^*\), and \(v\) and \(v^*\) are some eigenvectors of \(A, A^*\) respectively, in this paper a nice basis for \(V\) is found and the action of \(A, A^*\) on this basis in terms of six parameters is described.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 33D80
Mathematics Subject Classification ID: 05E35
Mathematics Subject Classification ID: 20G42
zbMATH DE Number: 2116544
zbMATH Keywords: tridiagonal pair
zbMATH Keywords: Leonard pair
zbMATH Keywords: \(q\)-Serre relations
zbMATH Keywords: basis
MaRDI profile type: Publication
full work available at URL: j.laa.2004.05.003
OpenAlex ID: W2032034122
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DOI: 10.1016/J.LAA.2004.05.003
description: scientific article; zbMATH DE number 2116544