Generic representations of orthogonal groups: the mixed functors

Abstract

In previous work, we defined the category of functors ${\mathcal{ℱ}}_{quad}$, 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 ${\mathcal{ℱ}}_{quad}$, 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 ${\mathcal{ℱ}}_{quad}$.