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arXiv · 1208.2380

Character correspondences for symmetric groups and wreath products

Anton Evseev
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Abstract

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 $S_p\wr S_w$. 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.

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Anton Evseev. 2012-08-11. Character correspondences for symmetric groups and wreath products. https://arxiv.org/abs/1208.2380

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