Generic representations of orthogonal groups: projective functors in the category Fquad

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126629In this paper, we continue the study of the category of functors Fquad, associated to F_2-vector spaces equipped with a nondegenerate quadratic form, initiated in two previous papers of the author. We define a filtration of the standard projective objects in Fquad; this refines to give a decomposition into indecomposable factors of the two first standard projective objects in Fquad. As an application of these two decompositions, we give a complete description of the polynomial functors of the category Fquad.32 pagesAlgebraic TopologyCategory Theory18A25; 16D90; 20C20Generic representations of orthogonal groups: projective functors in the category Fquadtext