Local structure of the p-blocks of \(\tilde S_ n\)
type: Item
instance of: scholarly article
title: Local structure of the p-blocks of \(\tilde S_ n\)
zbMATH Open document ID: 0646.20011
DOI: 10.1007/BF01162871
author: Marc Cabanes
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173941
review text: Local block theory was introduced by \textit{J. Alperin} and \textit{M. Broué} [Ann. Math., II. Ser. 110, 143-157 (1979; Zbl 0416.20006)] generalizing both ideas of R. Brauer and local analysis in finite group theory. The main concept in local block theory is the notion of subpairs of a block and inclusions between them. These objects were determined in the case of the symmetric groups by \textit{L. Puig} [Publ. Math. Univ. Paris VII 25, 171-189 (1987; Zbl 0639.20009)] and in the case of the general linear and unitary groups by \textit{M. Broué} [Astérisque 133/134, 159-187 (1986)]. In the present paper the author describes the subpairs and their inclusions (in odd characteristic) for the 2-fold covering groups of the symmetric groups. It turns out that the combinatorial algorithm of the removal of a p-bar has an algebraic interpretation as the inclusion of subpairs; this is similar to the case of the symmetric groups. A consequence of the results in this paper is a new proof of the Morris conjecture. This had been established earlier by \textit{J. F. Humphreys} [in J. Lond. Math. Soc., II. Ser. 33, 441-452 (1986; Zbl 0633.20007)] in a different way.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 4053887
zbMATH Keywords: local block theory
zbMATH Keywords: subpairs
zbMATH Keywords: inclusions
zbMATH Keywords: covering groups of the symmetric groups
zbMATH Keywords: p-bar
zbMATH Keywords: Morris conjecture
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
cites work: Local methods in block theory
cites work: Q3955560
cites work: Blocks of Projective Representations of the Symmetric Groups
cites work: The Spin Representation of the Symmetric Group
cites work: Q3781256
description: scientific article; zbMATH DE number 4053887