  Brane systems provide a large class of gauge theories that arise in string
theory. This paper demonstrates how such brane systems fit with a somewhat
exotic geometric object, called the affine Grassmannian. This gives a strong
motivation to study physical aspects of the affine Grassmannian. Explicit
quivers are presented throughout the paper, and a quiver addition algorithm to
generate the affine Grassmannian is introduced. An important outcome of this
study is a set of quivers for new elementary slices.
