On Fourier-Mukai transforms of upward flows for Hitchin systems

We consider the moduli space of semistable Higgs bundles on a smooth projective curve. Motivated by mirror symmetry, Hausel and Hitchin showed that over an open of the locus of smooth Hitchin fibers, the duality of Donagi-Pantev intertwines certain Lagrangian upward flows with hyperholomorphic vector bundles constructed from universal Higgs bundles. Using Arinkin's sheaf and some codimension estimates, we show a generalization of this result over the entire Hitchin base, for Higgs bundles of arbitrary degree.