  Recently Donkin defined signed Young modules as a simultaneous generalization
of Young and twisted Young modules for the symmetric group. We show that in odd
characteristic, if a Specht module $S^\lambda$ is irreducible, then $S^\lambda$
is a signed Young module. Thus the set of irreducible Specht modules coincides
with the set of irreducible signed Young modules. This provides evidence for
our conjecture that the signed Young modules are precisely the class of
indecomposable self-dual modules with Specht filtrations. The theorem is false
in characteristic two.
