The Structure of Indecomposable Injectives in Generic Representation Theory
نویسنده
چکیده
This paper considers the structure of the injective objects IVn in the category F of functors between F2-vector spaces. A co-Weyl object Jλ is defined, for each simple functor Fλ in 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 F are J-good. A finiteness result for proper sub-functors of coWeyl objects is proven, using the polynomial filtration of the shift functor ∆̃ : F → F . This research is motivated by the Artinian conjecture due to Kuhn, Lannes and Schwartz.
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