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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 ofS   p  ⁢  w${S_{pw}}$    and that ofS  p   ≀   S  w${S_{p}\wr S_{w}}$   . 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.

Character correspondences for symmetric groups and wreath products