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

Let Hn denote the Iwahori–Hecke algebra corresponding to the symmetric group Sn. We set up a Green correspondence for bimodules of these Hecke algebras, and a Brauer correspondence between their blocks. We examine Specht modules for Hn and compute the vertex of certain Specht modules, before using this to give a complete classification of the vertices of blocks of Hn in any characteristic. Finally, we apply this classification to resolve the Dipper–Du conjecture about the structure of vertices of indecomposable Hn‐modules.