The complexities of some simple modules of the symmetric groups

Details The complexities of some simple modules of the symmetric groups The complexities of some simple modules of the symmetric groups

2011-08-04

arxiv.org/abs/1108.1025v1

Mathematics

Representation Theory

Scientific paper

We show that the simple modules of the Rouquier blocks of symmetric groups,
in characteristic $p$ and having $p$-weight $w$ with $w < p$, have a common
complexity $w$. We also show that when $p$ is odd, $D^{(p+1,1^{p-1})}$ has
complexity 1, while the simple modules labelled by a partition having
$p$-weight 2 mostly have complexity 2.

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