Generic representations of orthogonal groups: the functor category Fquad
Christine Vespa
18A25, 16D90, 20C20
already submitted to Arxiv math.AT/0606484 with the title: the functor
category Fquad
Ecole Polytechnique Federale de Lausanne, Institut de Geometrie,
Algebre et Topologie, Lausanne, Switzerland.
christine.vespa@epfl.ch
In this paper, we define the functor category Fquad associated to vector
spaces over the field with two elements equipped with a quadratic
form. We show the existence of a fully-faithful, exact functor from F
to Fquad, which preserves simple objects, where F is the category of
functors from the category of finite dimensional vector spaces over the
field with two elements to the category of all vector spaces. We define
a subcategory Fquad, which is equivalent to the product of the
categories of modules over the orthogonal groups; the inclusion is a
fully-faithful functor which preserves simple objects.