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

Let ${\mathcal{H}}_n$ 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 ${\mathcal{H}}_n$ and compute the vertices of certain Specht modules, before using this to give a classification of the vertices of blocks of ${\mathcal{H}}_n$ in any characteristic. Finally, we apply this classification to resolve the Dipper-Du conjecture about the structure of vertices of indecomposable ${\mathcal{H}}_n$-modules.