Decomposable \(\lambda \)-critical tensors
type: Item
instance of: scholarly article
title: Decomposable \(\lambda \)-critical tensors
zbMATH Open document ID: 1196.15023
author: Rosário Fernandes
author: Henrique F.da Cruz
author: Fátima Rodrigues
published in: Linear Algebra and its Applications
publication date: 2010-05-21T00:00:00Z
review text: A partition \(\lambda=(\lambda_1,\dots,\lambda_s)\) of \(m\in \mathbb{N}^*\) and a finite dimensional vector space \(V\) over \(\mathbb{C}\) are considered. An irreducible character of the symmetric group of degree \(m\) \(S_m\) is identified with the corresponding partition \(\lambda\). \(V_{\lambda}\) denotes the symmetry class of tensors associated with \(\lambda\) and \(V\). For \(j\in\{1,\dots,\lambda_1\}\) and \(z\in V_{\lambda}\), the concepts of \(j\)-reach and \(j\)-annihilator of \(z\) are defined and they are used to introduce the notion of \(\lambda\)-critical elements of \(V_{\lambda}\). Some important properties of the \(\lambda\)-critical elements of \(V_{\lambda}\) are emphasized and they are used to characterize the decomposable elements of \(V_{\lambda}\) that are \(\lambda\)-critical. A family of generalized Plücker polynomials is constructed so that the set of their common roots includes the set of the families of components of decomposable \(\lambda\)-critical elements of \(V_{\lambda}\). These results extend the topics of the paper \textit{J. A. Dias da Silva} and \textit{F. Rodrigues} [Linear Algebra Appl. 414, No.~1, 172--198 (2006; Zbl 1090.15023)] to the framework of \(\lambda\)-critical tensors.
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 26C10
zbMATH DE Number: 5710791
zbMATH Keywords: decomposable tensors
zbMATH Keywords: \(\lambda\)-critical tensors
zbMATH Keywords: generalized Plücker polynomials
zbMATH Keywords: irreducible character
zbMATH Keywords: symmetric group
zbMATH Keywords: symmetry class of tensors
zbMATH Keywords: common roots
MaRDI profile type: Publication
full work available at URL: j.laa.2010.02.022
OpenAlex ID: W2769214068
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DOI: 10.1016/J.LAA.2010.02.022
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description: scientific article; zbMATH DE number 5710791