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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 29, Issue 3

# Character correspondences for symmetric groups and wreath products

Anton Evseev
• Corresponding author
• School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
• Email
• Other articles by this author:
Published Online: 2016-08-12 | DOI: https://doi.org/10.1515/forum-2013-0043

## 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.

MSC 2010: 20C30; 20C15

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Revised: 2015-10-28

Published Online: 2016-08-12

Published in Print: 2017-05-01

Funding Source: Engineering and Physical Sciences Research Council

Award identifier / Grant number: EP/G050244

The author was supported by the EPSRC Postdoctoral Fellowship EP/G050244.

Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 581–616, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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