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

Let H _n denote the Iwahori–Hecke algebra corresponding to the symmetric group 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 H _n and compute the vertex of certain Specht modules, before using this to give a complete classification of the vertices of blocks of H _n in any characteristic. Finally, we apply this classification to resolve the Dipper–Du conjecture about the structure of vertices of indecomposable H _n-modules.