The structure of indecomposable injectives in generic representation theory
Trans. Amer. Math. Soc. 350 (1998), 4167-4193.

Geoffrey M. L. Powell
LAGA, Institut Galil\'ee, Universit\'e Paris 13, 93430 Villetaneuse, France 

Abstract. This paper considers the structure of the injective objects 
$I_{V_n}$ in the category $\mathcal F$ of functors between 
$\mathbb F_2$-vector spaces. A co-Weyl object $J_\lambda$ is defined, for each
simple functor $F_\lambda$ in $\mathcal F$. A functor is defined to be 
$J$-good if it admits a finite filtration of which the quotients are co-Weyl 
objects. Properties of $J$-good functors are considered and it is shown that 
the indecomposable injectives in $\mathcal F$ are $J$-good. A finiteness 
result for proper sub-functors of co-Weyl objects is proven, using the 
polynomial filtration of the shift functor $\tilde\Delta:\mathcal F
\rightarrow\mathcal F$. This research is motivated by the Artinian conjecture 
due to Kuhn, Lannes and Schwartz.