Induced bases of symmetry classes of tensors

Let V^m? denote the mth tensor power of the finite dimensional complex vector space V. Let V_χ(G)?V^m? be the symmetry class of tensors corresponding to the permutation group G and the irreducible character χ of G. Each basis of V induces, in a natural way, a basis of V^m?. The article considers the corresponding problem of inducing bases of V_χ(G).