  We prove the Abelian/non-Abelian Correspondence with bundles for target
spaces that are partial flag bundles, combining and generalising results by
Ciocan-Fontanine-Kim-Sabbah, Brown, and Oh. From this we deduce how genus-zero
Gromov-Witten invariants change when a smooth projective variety X is blown up
in a complete intersection defined by convex line bundles. In the case where
the blow-up is Fano, our result gives closed-form expressions for certain
genus-zero invariants of the blow-up in terms of invariants of X. We also give
a reformulation of the Abelian/non-Abelian Correspondence in terms of
Givental's formalism, which may be of independent interest.
