Immanant preserving and immanant converting maps

We generalize a result in [G. Dolinar, P. Semrl, Determinant preserving maps on matrix algebras, Linear Algebra Appl. 348 (2002) 189–192], proving that if χ and λ are arbitrary irreducible complex characters of Sn and T : Mn(C) → Mn(C) is a surjective map satisfying dχ(T(A) + αT(B)) = dλ(A + αB), for all A, B Mn(C) and all α C, then T is linear. Our main theorem, combined with known results on linear preservers/converters of immanants, allows us to characterize the pairs (χ, λ) for which such maps exist and, in the cases they exist, to obtain the respective description.