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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
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Published Online: 2016-08-12 | DOI: https://doi.org/10.1515/forum-2013-0043


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 Spw and that of SpSw. 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.

Keywords: character; symmetric group; wreath product; McKay conjecture

MSC 2010: 20C30; 20C15


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About the article

Received: 2013-03-19

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, DOI: https://doi.org/10.1515/forum-2013-0043.

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