Orbifold Gromov-Witten theory of the symmetric product of A _r

Let A _r be the minimal resolution of the type A _r surface singularity. We study the equivariant orbifold Gromov-Witten theory of the n-fold symmetric product stack [Sym ⁿ(A _r)] of A _r. We calculate the divisor operators, which turn out to determine the entire theory under a nondegeneracy hypothesis. This, together with the results of Maulik and Oblomkov, shows that the Crepant Resolution Conjecture for Sym ⁿ(A _r) is valid. More strikingly, we complete a tetrahedron of equivalences relating the Gromov-Witten theories of [Sym ⁿ(A _r)]/Hilb ⁿ(A _r) and the relative Gromov-Witten/Donaldson-Thomas theories of A _r × P ¹.