Hemmer's conjecture on signed Young modules and self-dual Specht-filtered modules

Let $k$ be the underlying field, let $\N\in\operatorname{mod} k\Sigma_d$ be indecomposable and self-dual, and suppose that $N$ has a Specht, and hence also a dual Specht, filtration. Hemmer's conjecture. Then $N$ is isomorphic to a signed Young module. This conjecture concerns the classification of indecomposable self-dual modules admitting Specht filtrations; the paper provides evidence for it and proves the related result that irreducible Specht modules in odd characteristic are signed Young modules.