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

Christine Vespa ¹

¹ Institut de Recherche Mathématique Avancée Université Louis Pasteur 7 rue René Descartes 67084 Strasbourg Cédex, France

Fundamenta Mathematicae, Tome 200 (2008) no. 3, pp. 243-278

Résumé

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 ${\cal F}_{{\rm quad}}$.

Détail

DOI : 10.4064/fm200-3-2

Keywords: continue study category functors cal quad associated mathbb vector spaces equipped nondegenerate quadratic form initiated pure appl algebra algebr geom topology define filtration standard projective objects cal quad refines decomposition indecomposable factors first standard projective objects cal quad nbsp application these decompositions complete description polynomial functors cal quad