On the orthogonal bases of symmetry classes (Q1806105)

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 \(e_\alpha^*\).