On unstable modules over the Dickson algebras, the Singer functors R_sand the functors Fix_s

Abstract

On unstable modules over the Dickson algebras, the Singer functors R s and the functors Fix s GEOFFREY M L POWELLThe category D s ᐁ of unstable modules over the Steenrod algebra equipped with a compatible module structure over the Dickson algebra D s is studied at the prime 2, with applications to the Singer functor R s , considered as a functor from unstable modules ᐁ to D s ᐁ. An explicit copresentation of R s M is given using Lannes' Tfunctor when M is a reduced unstable module; applying Lannes' functor Fix s , this is used to show that R s gives a fully-faithful embedding of ᐁ in D s ᐁ. In addition, the right adjoint Z s to R s is introduced and is related to the indecomposables functor and the functor Fix s .