Character correspondences for symmetric groups and wreath products

2012/08/11 by Evseev, Anton
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1208.2380

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.

Related

• Alperin-McKay natural correspondences in solvable and symmetric groups for the prime p=2
• A Relationship Between Character Values Of Wreath Products And The Symmetric Group
• New refinements of the McKay conjecture for arbitrary finite groups
• On characters of wreath products
• The Alperin Weight Conjecture and the Glauberman correspondence via character triples