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

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

2007-04-04

arxiv.org/abs/0704.0502v1

Mathematics

Algebraic Topology

32 pages

Scientific paper

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 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.

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