We compute the C*-equivariant quantum cohomology ring of Y, the
minimal resolution of the DuVal singularity C^2/G where G is a finite
subgroup of SU(2). The quantum product is expressed in terms of an ADE
root system canonically associated to G. We generalize the resulting
Frobenius manifold to non-simply laced root systems to obtain an n
parameter family of algebra structures on the affine root lattice of
any root system. Using the Crepant Resolution Conjecture, we obtain a
prediction for the orbifold Gromov-Witten potential of [C^2/G].