  We provide a natural geometric setting for symmetric Howe duality. This is
realized as a (loop) sl(n) action on derived categories of coherent sheaves on
certain varieties arising in the geometry of the Beilinson-Drinfeld
Grassmannian.
  The main construction parallels our earlier work on categorical sl(n) actions
and skew Howe duality. In that case the varieties involved arose in the
geometry of the affine Grassmannian. We discuss some relationships between the
two actions.
