A note on the orthogonal basis of a certain full symmetry class of tensors.
type: Item
instance of: scholarly article
title: A note on the orthogonal basis of a certain full symmetry class of tensors.
zbMATH Open document ID: 1034.15009
DOI: 10.1016/S0024-3795(03)00426-9
author: M. R. Pournaki
author: Astrid Reifegerste
author: Christine Bessenrodt
published in: Linear Algebra and its Applications
publication date: 2003-08-25T00:00:00Z
review text: Let \([\lambda]\) denote the irreducible character of a partition \(\lambda=(\lambda_1,\ldots,\lambda_l)\), where \(\lambda_1\geq\cdots\geq\lambda_l>0\) is a weakly decreasing sequence of integers with \(\sum_{i=1}^l\lambda_i=n\). The authors show that the full symmetry class of tensors associated with the irreducible character \([2,1^{n-2}]\) of \(S_n\) does not have an orthogonal basis consisting of decomposable symmetrized tensors.
reviewed by: Nikolai I. Osetinski
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 1970631
zbMATH Keywords: symmetry class of tensors
zbMATH Keywords: orthogonal basis
zbMATH Keywords: decomposable symmetrized tensors
zbMATH Keywords: irreducible characters of the symmetric group
MaRDI profile type: Publication
cites work: Computation of the dimensions of symmetry classes of tensors associated with the finite two dimensional projective special linear group
cites work: On the orthogonal basis of the symmetry classes of tensors associated with the dicyclic group
cites work: Inequalities for generalized matrix functions based on arbitrary characters
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cites work: Symmetry classes of tensors associated with certain groups
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cites work: On the orthogonal basis of the symmetry classes of tensors associated with certain characters
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description: scientific article; zbMATH DE number 1970631