Generic representations of orthogonal groups: projective functors in the category ${\cal F}_{\rm quad}$
Tom 200 / 2008
Fundamenta Mathematicae 200 (2008), 243-278
MSC: 18A25, 20J99, 16D90, 20C20.
DOI: 10.4064/fm200-3-2
Streszczenie
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 ${\cal F}_{{\rm quad}}$.
