Generic representations of orthogonal groups: projective functors in the category ${\cal F}_{\rm quad}$

Volume 200 / 2008

Christine Vespa Fundamenta Mathematicae 200 (2008), 243-278 MSC: 18A25, 20J99, 16D90, 20C20. DOI: 10.4064/fm200-3-2

Abstract

We continue the study of the category of functors ${\cal F}_{{\rm quad}}$, associated to ${\mathbb F}_2$-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in ${\cal F}_{{\rm quad}}$; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in ${\cal F}_{{\rm quad}}$: $P_{H_0}$ and $P_{H_1}$. As an application of these two decompositions, we give a complete description of the polynomial functors in ${\cal F}_{{\rm quad}}$.

Authors

  • Christine VespaInstitut de Recherche Mathématique Avancée
    Université Louis Pasteur
    7 rue René Descartes
    67084 Strasbourg Cédex, France
    e-mail

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