Some non-trivial symmetry classes of tensors associated with certain characters (Q699942)

Let \(G\) be a subgroup of the symmetric group \(S_n\). Let \(V\) be a finite-dimensional vector space over the complex field \(\mathbb{C}\). Let \(V^n_\chi(G)\) denote the symmetry class of tensors associated with \(G\) and \(\chi\). In the paper under review the author proves that if \(\chi\) is any irreducible constituent of the permutation character of \(G\) on \(n\) letters, then \(V^n_\chi(G)\neq 0\).