On defect groups for generalized blocks of the symmetric group

Details On defect groups for generalized blocks of the symmetric group On defect groups for generalized blocks of the symmetric group

2007-03-06

arxiv.org/abs/math/0703157v2

Mathematics

Representation Theory

18 pages

Scientific paper

In a paper of 2003, B. K\"ulshammer, J. B. Olsson and G. R. Robinson defined
$\ell$-blocks for the symmetric groups, where $\ell >1$ is an arbitrary
integer. In this paper, we give a definition for the defect group of the
principal $\ell$-block. We then check that, in the Abelian case, we have an
analogue of one of M. Brou\'e's conjectures.

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