James classified the simple modules over the group algebra
using modules
denoted
, where
is a partition of
. In particular, he showed
that
is simple or zero
for every partition
and, furthermore, that for every simple
-module
there exists a partition
such that
. This
paper is an extension of a paper of Dodge and Ellers in which they studied analogous modules
over the centralizer
algebra
,
where
is a
partition of
and
a partition
of
. For every
positive prime
we find counterexamples to their conjecture that the
-modules
are always simple or
zero, where
is a field of
characteristic . We also study
the relationship between
and
in special cases.