We continue the study of the category of functors , associated to 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 ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in : and . As an application of these two decompositions, we give a complete description of the polynomial functors in .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-3-2,
author = {Christine Vespa},
title = {Generic representations of orthogonal groups: projective functors in the category $F\_{quad}$
},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {243-278},
zbl = {1147.18002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-3-2}
}
Christine Vespa. Generic representations of orthogonal groups: projective functors in the category $ℱ_{quad}$
. Fundamenta Mathematicae, Tome 201 (2008) pp. 243-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-3-2/