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On the orthogonal bases of symmetry classes. (English) Zbl 0935.15024
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)

MSC:
15A72 Vector and tensor algebra, theory of invariants
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References:
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