Cyclic Hodge integrals and loop Schur functions

We conjecture an evaluation of three-partition cyclic Hodge integrals in terms of loop Schur functions. Our formula implies the orbifold Gromov-Witten/Donaldson-Thomas correspondence for toric Calabi-Yau threefolds with transverse An singularities. We prove the formula in the case where one of the partitions is empty, and thus establish the orbifold Gromov-Witten/Donaldson-Thomas correspondence for local toric surfaces with transverse An singularities.