  A map between string junctions in the affine 7-brane backgrounds and vector
bundles on del Pezzo surfaces is constructed using mirror symmetry. It is shown
that the lattice of string junctions with support on an affine 7-brane
configuration is isomorphic to the K-theory group of the corresponding del
Pezzo surface. This isomorphism allows us to construct a map between the states
of the N=2, D=4 theories with E_N global symmetry realized in two different
ways in Type IIB and Type IIA string theory. A subgroup of the SL(2,Z) symmetry
of the \hat{E}_9 7-brane background appears as the Fourier-Mukai transform
acting on the D-brane configurations realizing vector bundles on elliptically
fibered B_9.
