arXiv subjects
Publications and source records attributed to Christine Vespa.
In previous work, we defined the category of functors Fquad, associated to vector spaces over the field with two elements equipped with a nondegenerate quadratic form. In this paper, we define a special family of objects in the category Fquad, 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 Fquad.
In this paper, we define the functor category Fquad associated to vector spaces over the field with two elements, F\_2, equipped with a quadratic form. We show the existence of a fully-faithful, exact functor ι: \F \to Fquad, which preserves simple objects, where \F is the category of functors from the category of finite dimensional F\_2-vector spaces to the category of all F\_2-vector spaces. We define the subcategory Fiso of Fquad, which is equivalent to the product of the categories of modules over the orthogonal groups; the inclusion is a fully-faithful functor κ: Fiso \to Fquad which preserves simple objects.