Linear groups associated with elements of a group algebra
Let K be a field, \(M_ m(K)\) the \(m\times m\) matrices with entries in K, and \(S_ m\) the symmetric group of degree m. If c is a function from \(S_ m\) to K, let \(d_ c(A)=\sum_{\sigma \in S_ m}c(\sigma)\prod^{m}_{i=1}A_{i,\sigma (i)}\) and let S(c) be the group of non-singular matrices B satisfying \(d_ c(BX)=d_ c(X)\) for all \(X\in M_ m(K)\). S(c) gives information about the problem of determining conditions for equality of decomposible symmetric tensors. The authors give necessary and sufficient conditions for a matrix to belong to S(c). In addition, they find properties that matrices which belong to S(c) satisfy.
scientific article; zbMATH DE number 4023562