\title{The complexity of the Specht modules corresponding to hook partitions}
\author{Kay Jin Lim}

\maketitle
\begin{abstract} We show that the complexity of the Specht module
corresponding to any hook partition is the $p$-weight of the
partition. We calculate the variety and the complexity of the signed
permutation modules. Let $E_s$ be a representative of the conjugacy class containing an elementary abelian $p$-subgroup of a symme
tric group generated by $s$ disjoint $p$-cycles. We give formulae for the generic Jordan types of signed permutation modules
restricted to $E_s$ and of Specht modules corresponding to hook
partitions $\mu$ restricted to $E_s$, especially for the case where
$s$ is the $p$-weight of $\mu$.
\end{abstract}