Variation of induced linear operators

Let V be an n-dimensional inner product space. Let λ be an irreducible character of the symmetric group Sm, and let Vλ be the symmetry class of tensors associated with it. Let A be a linear operator on V and let Kλ (A) be the operator it induces on Vλ . We obtain an explicit expression for the norm of the derivative of the map A→Kλ (A) in terms of the singular values of A. Two special cases of this problem-antisymmetric and symmetric tensor products-have been studied earlier, and our results reduce to the earlier ones in these cases