On a permutation character of S_m

Let G be a permutation group on in elements and K be an n-dimensional complex vector space. Then G acts naturally on ⊗^mV, namely, V₁ ⊗ ⋯ × v_m → vg^-1(1) ⊗ ⋯ ⊗ vg^-1(m) · In this expository article, we obtain the well known irreducible constituents of this representation of G by an approach that is both elegant and economical.