The structure of indecomposable injectives in generic representation theory
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 Trans. Amer. Math. Soc. 350 (1998), 41674193 Request permission
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 coWeyl 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 coWeyl 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 subfunctors of coWeyl 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.References

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Additional Information
 Geoffrey M. L. Powell
 Affiliation: LAGA, Institut Galilée, Université Paris 13, 93430 Villetaneuse, France
 Email: powell@math.univparis13.fr
 Received by editor(s): December 5, 1996
 Additional Notes: The author was supported by a Royal Society (GB) ESEP fellowship at the Institut Galilée, Université de ParisNord, France during the preparation of this work. The final version was prepared whilst the author was a visitor at the University of Virginia, Charlottesville
 © Copyright 1998 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 350 (1998), 41674193
 MSC (1991): Primary 18G05, 20G40, 55S10
 DOI: https://doi.org/10.1090/S0002994798021254
 MathSciNet review: 1458333