Towards a Global Springer Theory I: The affine Weyl group action

Details Towards a Global Springer Theory I: The affine Weyl group action Towards a Global Springer Theory I: The affine Weyl group action

2008-10-13

arxiv.org/abs/0810.2146v4

Mathematics

Algebraic Geometry

39 page; containing an introduction for the three papers in this series; materials re-organized

Scientific paper

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.

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