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.
Categories: math.RT