Global Springer theory

@article{Yun2011GlobalST,
  title={Global Springer theory},
  author={Zhiwei Yun},
  journal={Advances in Mathematics},
  year={2011},
  volume={228},
  pages={266-328}
}
  • Zhiwei Yun
  • Published 2011
  • Mathematics
  • Advances in Mathematics
Abstract We generalize 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 graded double affine Hecke algebra (DAHA) on the direct image complex of the parabolic Hitchin fibration. In particular, we get representations of the degenerate graded DAHA on the cohomology of parabolic Hitchin fibers, providing the first step towards a global… Expand
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References

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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 parabolicExpand
Towards a Global Springer Theory II: the double affine action
We construct an action of the graded double affine Hecke algebra (DAHA) on the parabolic Hitchin complex, extending the affine Weyl group action constructed in \cite{GSI}. In particular, we getExpand
Langlands duality and global Springer theory
Abstract We compare the cohomology of (parabolic) Hitchin fibers for Langlands dual groups G and G∨. The comparison theorem fits in the framework of the global Springer theory developed by theExpand
Towards a Global Springer Theory III: Endoscopy and Langlands duality
We prove three new results about the global Springer action defined in \cite{GSI}. The first one determines the support of the perverse cohomology sheaves of the parabolic Hitchin complex, whichExpand
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