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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The structure of indecomposable injectives in generic representation theory
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by Geoffrey M. L. Powell PDF
Trans. Amer. Math. Soc. 350 (1998), 4167-4193 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 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
  • 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
  • © Copyright 1998 American Mathematical Society
  • 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