On the dimensions of cyclic symmetry classes of tensors
type: Item
instance of: scholarly article
title: On the dimensions of cyclic symmetry classes of tensors
zbMATH Open document ID: 0924.20005
author: M. R. Pournaki
author: M. R. Darafsheh
published in: Journal of Algebra
publication date: 1999-09-14T00:00:00Z
review text: Let \(V\) be an \(n\)-dimensional complex vector space and suppose \(V^{\otimes m}\) is equipped with the standard action of the symmetric group \(S_m\) permuting the factors. If \(G\) is a subgroup of \(S_m\) one associates to \(G\) the symmetry class of tensors \(T(G,\chi)\), where \(\chi\) is a character. The authors study the case when \(G\) is a cyclic group. The main result of the paper under review relates the dimension of the symmetry class of tensors in a very nice way with a natural generalization of the Ramanujan sum \(C_m(h)=\sum\exp(2\pi iht/m)\), the summation running over all \(t\), \(1\leq t\leq m-1\), and \((t,m)=1\).
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 11P99
zbMATH DE Number: 1218718
zbMATH Keywords: symmetry classes of tensors
zbMATH Keywords: Ramanujan sums
zbMATH Keywords: actions of symmetric groups
zbMATH Keywords: characters
reviewed by: Plamen Koshlukov
MaRDI profile type: Publication
full work available at URL: jabr.1997.7376
OpenAlex ID: W1997009520
cites work: Q4101884
cites work: Cyclic symmetry classes
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cites work: Q4771383
cites work: The dimensions of certain symmetry classes of tensors II
cites work: Q4053787
cites work: On the cyclic symmetry classes
DOI: 10.1006/JABR.1997.7376
description: scientific article; zbMATH DE number 1218718