On the equality of families of decomposable symmetrized tensors (Q1963925)

Let \(S_m\) be symmetric group of degree \(m\). The decomposable symmetrized tensor is denoted by \(x_1* \dots*x_m\). The aim of this paper is to present some necessary and equivalent conditions for \(x_{\sigma (1)}* \dots*x_{\sigma (m)}=y_{\sigma(1)} *\dots*y_{\sigma(m)}\) to hold, for all \(\sigma\in S_m\), in arbitrary symmetric classes of tensors. The paper contains the sections ``The rank partition and transversal flag''; ``The multilinearity partition and vanishing of decomposable symmetrized tensors''; and ``The equality of decomposable symmetrized tensors''.