Non-vanishing and orthogonal basis of symmetry classes of tensors (Q5929662)

Let \(\chi\) be any irreducible complex character of \(G\) and let \(V^n_\chi(G)\) denote the symmetry classes of tensors associated with \(G\) and \(\chi\). In the light of the Cayley representation of \(G\), the paper describes a formula for the dimension of \(V^n_\chi(G)\) and discusses its nonvanishing in general. A necessary condition for the existence of an orthogonal basis of decomposable symmetrized tensors for \(V^n_\chi(G)\) is also obtained.