  We propose a generalization of Springer representations to the context of
groups over a global function field. The global counterpart of the Grothendieck
simultaneous resolution is the parabolic Hitchin fibration. We construct an
action of the affine Weyl group on the direct image complex of the parabolic
Hitchin fibration. In particular, we get representations of the affine Weyl
group on the cohomology of parabolic Hitchin fibers, providing the first step
towards a global Springer theory.
