Sous-objets deI ⊗ Λndans la catégorie des foncteurs entre [formula omitted]2-espaces vectoriels

Abstract

Listen

Translate article

Let F denote the abelian category of functors from finite-dimensional F2-vector spaces to F2-vector spaces. We are concerned with the artinian conjecture, which states that the injective functorsIEare artinian objects in F for each finite dimensional F2-vector spaceE. This is true for dimE=1 and has been recently proven for dimE=2. This paper gives one of the arguments of this proof: we produce a sequence of objects of F,K̄n, whose subobjects are finite in a sense that generalizes the case dimE=1. The main ingredients are the behaviour of the difference functor on Weyl functors and simple functors, and the computation of some extension groups.