When Polarizations Generate

Let G be a reductive complex algebraic group and V a finite-dimensional G-module. From elements of the invariant algebra C[V]^G we obtain by polarization elements of C[kV]^G, where k\geq 1 and kV denotes the direct sum of k copies of V. For G simple our main result is the classification of the G-modules V and integers k\geq 2 such that polarizations generate C[kV]^G.