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

2007/04/04 by Christine Vespa, Vespa, Christine
Mathematics · #16D90 #18A25 #20C20 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #math.AT #math.CT #msc:16D90 #msc:18A25 #msc:20C20

paper · pdf · doi:10.48550/arxiv.0704.0502

32 pages

arxiv created 2007/04/04 · arxiv updated 2009/12/01

Abstract

In this paper, we continue the study of the category of functors Fquad, associated to F₂-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.

Related

• The functor category Fquad
• C₂-Equivariant Orthogonal Calculus
• Polynomial functors on flags
• Polynomial functors on some categories of elements
• Polynomial Functors on Pointed Categories