Green correspondence for Mackey functors

Abstract

The Green corespondence for modules of group algebras was introduced by Green in 1964. A version for Mackey functors was introduced by Sasaki in 1982. Sasaki’s characterization of Mackey functor correspondence was based on the theory of Green functors. In this thesis, we give Sasaki’s characterization and an alternative characterization of the Mackey functor correspondence. Our characterization is closer to Green’s original module theoretic approach. We show that the two characterizations are equivalent. This yields a new way of determining vertices, sources and Green correspondents; we shall illustrate this with some examples.