Shahryari, M. On the orthogonal bases of symmetry classes. (English) Zbl 0935.15024 J. Algebra 220, No. 1, 327-332 (1999). Let \(V\) be an \(n\)-dimensional complex inner product space and let \(\{e_1,\dots,e_n\}\) be an orthonormal basis of \(V\). Suppose \(G\) is a permutation group of degree \(m\) and \(X\) is an irreducible character of \(G\). The symmetry class of tensors associated with \(G\) and \(X\) is denoted by \(V_X(G)\). This note contains one major theorem. The author discusses the problem of existing orthogonal bases for \(V_X(G)\) consisting of symmetrized decomposable tensors \(e_\alpha^*\). Reviewer: Y.Kuo (Knoxville) Cited in 7 Documents MSC: 15A72 Vector and tensor algebra, theory of invariants Keywords:complex inner product space; orthonormal basis; permutation group; symmetry class of tensors; symmetrized decomposable tensors PDF BibTeX XML Cite \textit{M. Shahryari}, J. Algebra 220, No. 1, 327--332 (1999; Zbl 0935.15024) Full Text: DOI References: [1] Freese, R., Inequalities for generalized matrix functions based on arbitrary characters, Linear algebra appl., 7, 337-345, (1973) · Zbl 0283.15004 [2] Holmes, R.R., Orthogonal bases of symmetrized tensor spaces, Linear and multilinear algebra, 39, 241-243, (1995) · Zbl 0831.15018 [3] Holmes, R.R.; Tam, T.Y., Symmetry classes of tensors associated with certain groups, Linear and multilinear algebra, 32, 21-31, (1992) · Zbl 0762.15015 [4] Marcus, M., Finite dimensional multilinear algebra, part I, (1973), Dekker New York · Zbl 0284.15024 [5] Merris, R., Recent advances in symmetry classes of tensors, Linear and multilinear algebra, 7, 317-328, (1979) · Zbl 0418.15021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.