#### Volume 7, issue 1 (2007)

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Generic representations of orthogonal groups: the mixed functors

### Christine Vespa

Algebraic & Geometric Topology 7 (2007) 379–410
 arXiv: math.AT/0611560
##### Abstract

In previous work, we defined the category of functors ${\mathsc{ℱ}}_{quad}$, associated to ${\mathbb{F}}_{2}$–vector spaces equipped with a nondegenerate quadratic form. In this paper, we define a special family of objects in the category ${\mathsc{ℱ}}_{quad}$, named the mixed functors. We give the complete decompositions of two elements of this family that give rise to two new infinite families of simple objects in the category ${\mathsc{ℱ}}_{quad}$.

##### Keywords
functor categories, quadratic forms over $\mathbb{F}_2$
##### Mathematical Subject Classification 2000
Primary: 18A25
Secondary: 16D90, 20C20