The green correspondents of simple group modules

AbstractWe shall show that these correspondents are not arbitrary modules, but have a strong property with respect to specializations (see Corollary 2.8) which ensures that they belong to a family of modules that are theoretically classifiable using only local information about the group (see Corollary 3.12 and the remarks following it). This extends to arbitrary simple modular group modules the similar properties proven in [2] for such modules lying in blocks with trivial intersection defect groups. Indeed, we lean heavily on [2], and follow its notation as much as possible. As an addendum we indicate in Section 4 how our results can be extended from Green correspondents to sources of simple group modules