Vertices for Iwahori-Hecke algebras and the Dipper-Du conjecture

Let $\mathscr{H}_n$ denote the Iwahori-Hecke algebra corresponding to the symmetric group $\mathfrak{S}_n$. We set up a Green correspondence for bimodules of these Hecke algebras, and a Brauer correspondence between their blocks. We examine Specht modules for $\mathscr{H}_n$ and compute the vertices of certain Specht modules, before using this to give a classification of the vertices of blocks of $\mathscr{H}_n$ in any characteristic. Finally, we apply this classification to resolve the Dipper-Du conjecture about the structure of vertices of indecomposable $\mathscr{H}_n$-modules.