A note on the orthogonal basis of a certain full symmetry class of tensors.
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.
irreducible characters of the symmetric group
scientific article; zbMATH DE number 1970631