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 10 September 2011
  • Mathematics
  • Advances in Mathematics
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A BSTRACT . Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the
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Generalised Springer correspondence for Z/m-graded Lie algebras
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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 parabolic
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 get
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 the
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, which
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