  We study the relative Donaldson-Thomas theory of A_n x P^1, where A_n is the
surface resolution of a type A_n singularity. The action of divisor operators
in the theory is expressed in terms of operators of the affine algebra
\hat{gl}(n+1) on Fock space. Assuming a nondegeneracy conjecture, this gives a
complete solution for the theory. The results complete the comparison of this
theory with the Gromov-Witten theory of A_n x P^1 and the quantum cohomology of
the Hilbert scheme of points on A_n.
