  We study the topological group structure (coming from loop multiplication) on
an affine Grassmannian. In particular, we study finite-dimensional subvarieties
that generate the homology ring. We show that there is a canonical family of
generating Schubert varieties, namely those defined by the negative of the
coroot associated to the highest root. These not only generate the homology,
but generate the affine Grassmannian itself in a precise sense.
