Towards a Global Springer Theory I: The affine Weyl group action
Algebraic Geometry
2009-04-22 v4 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0810.2146,
title = {Towards a Global Springer Theory I: The affine Weyl group action},
author = {Zhiwei Yun},
journal= {arXiv preprint arXiv:0810.2146},
year = {2009}
}
Comments
39 page; containing an introduction for the three papers in this series; materials re-organized