arXiv subjects
Publications and source records attributed to Craig J. Dodge.
We present (with proof) a new family of decomposable Specht modules for the symmetric group in characteristic 2. These Specht modules are labelled by partitions of the form $(a,3,1^b)$, and are the first new examples found for thirty years. Our method of proof is to exhibit summands isomorphic to irreducible Specht modules, by constructing explicit homomorphisms between Specht modules.
Let $F$ be a field of characteristic $p$. We show that $\Hom_{FΣ_n}(S^λ, S^μ)$ can have arbitrarily large dimension as $n$ and $p$ grow, where $S^λ$ and $S^μ$ are Specht modules for the symmetric group $Σ_n$. Similar results hold for the Weyl modules of the general linear group. Every previously computed example has been at most one-dimensional, with the exception of Specht modules over a field of characteristic two. The proof uses the work of Chuang and Tan, providing detailed information about the radical series of Weyl modules in Rouquier blocks.