Variation of induced linear operators Original Research Article

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.