  We give geometric descriptions of the category C_k(n,d) of rational
polynomial representations of GL_n over a field k of degree d for d less than
or equal to n, the Schur functor and Schur-Weyl duality. The descriptions and
proofs use a modular version of Springer theory and relationships between the
equivariant geometry of the affine Grassmannian and the nilpotent cone for the
general linear groups. Motivated by this description, we propose
generalizations for an arbitrary connected complex reductive group of the
category C_k(n,d) and the Schur functor.
