  Brown proved that the I-function of a toric fibration lies on the overruled
Lagrangian cone of its genus zero Gromov-Witten theory, introduced by Coates
and Givental. In this paper, we prove the theorem for partial flag variety
fibrations. To do so, we will construct new moduli spaces generalising the idea
of Ciocan-Fontanine, Kim and Maulik.
