Categorical geometric symmetric Howe duality

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.