  We show that two Weyl group actions on the Springer sheaf with arbitrary
coefficients, one defined by Fourier transform and one by restriction, agree up
to a twist by the sign character. This generalizes a familiar result from the
setting of l-adic cohomology, making it applicable to modular representation
theory. We use the Weyl group actions to define a Springer correspondence in
this generality, and identify the zero weight spaces of small representations
in terms of this Springer correspondence.
