Root Systems and the Quantum Cohomology of Ade Resolutions
نویسنده
چکیده
We compute the C∗-equivariant quantum cohomology ring of Y , the minimal resolution of the DuVal singularity C/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/G].
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