  We categorify the R-matrix isomorphism between tensor products of minuscule
representations of U_q(sl(n)) by constructing an equivalence between the
derived categories of coherent sheaves on the corresponding convolution
products in the affine Grassmannian. The main step in the construction is a
categorification of representations of U_q(sl(2)) which are related to
representations of U_q(sl(n)) by quantum skew Howe duality. The resulting
equivalence is part of the program of algebro-geometric categorification of
Reshitikhin-Turaev tangle invariants developed by the first two authors.
