Two commuting operators associated with a tridiagonal pair
type: Item
instance of: scholarly article
title: Two commuting operators associated with a tridiagonal pair
zbMATH Open document ID: 1244.15009
author: Sarah Bockting-Conrad
published in: Linear Algebra and its Applications
publication date: 2012-05-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1110.3434
review text: Let \(V\) be a finite-dimensional vector space over a field. The author considers an ordered pair of linear transformations \(A:V\to V\) and \(A^*:V\to V\) that satisfy certain conditions. The pair \((A, A^*)\) is called a tridiagonal pair. It is shown that there exist unique linear transformations \(\Delta :V\to V\), \(\Psi :V\to V\) that satisfy specific properties. Furthermore, these transformations are characterized by the fact that they commute.
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 6034527
zbMATH Keywords: tridiagonal pair
zbMATH Keywords: Leonard pair
zbMATH Keywords: \(q\)-Serre relations
zbMATH Keywords: commuting operators
zbMATH Keywords: linear transformations
reviewed by: Andreas Arvanitoyeorgos
MaRDI profile type: Publication
OpenAlex ID: W1971822416
arXiv ID: 1110.3434
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DOI: 10.1016/J.LAA.2012.02.007
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description: scientific article; zbMATH DE number 6034527