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La catégorie Fquad des foncteurs de Mackey généralisés pour les formes quadratiques sur F_2

Abstract : The purpose of this work is to construct and study functor categories associated to F_2-vector spaces equipped with a quadratic form. After the construction of the category Fquad by use of similar techniques as for Mackey functors, we obtain several results about simple objects of this category.

We prove the existence of a faithful, exact functor, noted by i, from F to Fquad, which preserves simple objects, where F is the category of functors from the category of finite F_2-vector spaces to the category of all vector spaces.

We introduce another functor category, noted by Fiso, whose simple objects are indexed by the irreducible modular representations of possibly degenerate orthogonal groups over F_2 and we prove the existence of a faithful, exact functor, noted by k, from Fiso to Fquad, which preserves simple objects.

Using the decomposition of the first two projective generators of the category Fquad, we obtain a classification of the simple objects of lowest rank of Fquad, which allows us to prove that the polynomial functors of Fquad are in the image of the functor i. In the decomposition of these projective generators appear new functors of Fquad, called mixed functors, which give two infinite families of simple objects of Fquad, which do not arise from the categories F and Fiso.
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https://tel.archives-ouvertes.fr/tel-00011892
Contributor : Christine Vespa <>
Submitted on : Thursday, March 9, 2006 - 3:31:41 PM
Last modification on : Tuesday, October 20, 2020 - 3:56:18 PM
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Christine Vespa. La catégorie Fquad des foncteurs de Mackey généralisés pour les formes quadratiques sur F_2. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2005. Français. ⟨tel-00011892⟩

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