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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The structure of indecomposable injectives
in generic representation theory


Author: Geoffrey M. L. Powell
Journal: Trans. Amer. Math. Soc. 350 (1998), 4167-4193
MSC (1991): Primary 18G05, 20G40, 55S10
DOI: https://doi.org/10.1090/S0002-9947-98-02125-4
MathSciNet review: 1458333
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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.


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Additional Information

Geoffrey M. L. Powell
Affiliation: LAGA, Institut Galilée, Université Paris 13, 93430 Villetaneuse, France
Email: powell@math.univ-paris13.fr

DOI: https://doi.org/10.1090/S0002-9947-98-02125-4
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 Paris-Nord, France during the preparation of this work. The final version was prepared whilst the author was a visitor at the University of Virginia, Charlottesville
Article copyright: © Copyright 1998 American Mathematical Society