Shimura Varieties and Trace Formula Seminar

I propose an analogue of Springer representations when the finite field in the classical version is replaced by a global function field. The Grothendieck-Springer alternation will be replaced by the so-called parabolic Hitchin fibration. I will construct an action of the affine Weyl group on the direct image complex of the parabolic Hitchin fibration. I will also discuss examples in SL(2) to illustrate properties of these global Springer representations.