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In 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 thestandard projective objects in Fquad; this refines to give a decomposition intoindecomposable factors of the two first standard projective objects in Fquad.As an application of these two decompositions, we give a complete descriptionof the polynomial functors of the category Fquad.

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