Diagrams for Young modules over $\mathbb{F}_2$.

Young modules are the indecomposable summands of the permutation modules for the symmetric group $S_n$, on the cosets of the Young subgroups $S_\lambda$. They are irreducible over fields of characteristic 0, where they coincide with the Specht modules, but over fields of positive characteristic their structure is more complicated, and less well understood. In this talk I will describe the construction of module diagrams for the Young modules over $\FF_2$ up to the symmetric group $S_7$. The information in these diagrams allows a complete determination of the submodule lattices, but presents it in a more compact form. I will explain the meaning of these diagrams and the computational methods used.