Character correspondences for symmetric groups and wreath products

The Alperin-McKay conjecture relates irreducible characters of a block of an arbitrary finite group to those of its p-local subgroups. A refinement of this conjecture was stated by the author in a previous paper. We prove that this refinement holds for all blocks of symmetric groups. Along the way we identify a "canonical" isometry between the principal block of S-pw and that of S-p similar to S-w. We also prove a general theorem on expressing virtual characters of wreath products in terms of certain induced characters. Much of the paper generalises character-theoretic results on blocks of symmetric groups with abelian defect and related wreath products to the case of arbitrary defect.