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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39 Citations
Highly Influential Citations
9
Background Citations
12
Methods Citations
10
Results Citations
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39 Citations

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The spherical part of the local and global Springer actions
The affine Weyl group acts on the cohomology (with compact support) of affine Springer fibers (local Springer theory) and of parabolic Hitchin fibers (global Springer theory). In this paper, we show…
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…
A global analogue of the Springer resolution for SL2
The global nilpotent cone N is a singular stack associated to the choice of an algebraic group G, a smooth projective curve X, and a line bundle L on X, which is of fundamental importance to the…
Ginzburg algebras and the Hitchin connection for parabolic G-bundles
For a simple, simply connected, complex group G, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic…
Hilbert schemes on plane curve singularities are generalized affine Springer fibers
In this paper, we show that Hilbert schemes of planar curve singularities can be interpreted as generalized affine Springer fibers for $GL_n$. This leads to a construction of a rational Cherednik…
Affine Springer Fibers, Procesi bundles, and Cherednik algebras
Let g be a semisimple Lie algebra, t its Cartan subalgebra and W the Weyl group. The goal of this paper is to prove an isomorphism between suitable completions of the equivariant Borel-Moore homology…
The affine Springer fiber - sheaf correspondence
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…
Perverse sheaves on infinite-dimensional stacks, and affine Springer theory
The goal of this work is to construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the loop Lie algebra Lg and to show that the affine Grothendieck-Springer…
Mixed categories, formality for the nilpotent cone, and a derived Springer correspondence
Generalised Springer correspondence for Z/m-graded Lie algebras
We establish a generalised Springer correspondence for Z/m-graded Lie algebras and degenerate double affine Hecke algebras, in the framework recently developped by Lusztig and Yun.
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References

SHOWING 1-10 OF 39 REFERENCES
Towards a Global Springer Theory I: The affine Weyl group action
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…
Fixed point varieties on affine flag manifolds
We study the space of Iwahori subalgebras containing a given element of a semisimple Lie algebra over C((ɛ)). We also define and study a map from nilpotent orbits in a semisimple Lie algebra over C…
Conformal blocks and generalized theta functions
LetSUXr be the moduli space of rankr vector bundles with trivial determinant on a Riemann surfaceX. This space carries a natural line bundle, the determinant line bundleL. We describe a canonical…
Codimensions of root valuation strata
This paper defines and studies a stratification of the adjoint quotient of the Lie algebra of a reductive group over a Laurent power series field. The stratification arises naturally in the context…
Finite-dimensional representations of DAHA and affine Springer fibers: The spherical case
We classify finite dimensional simple spherical representations of rational double affine Hecke algebras, and we study a remarkable family of finite dimensional simple spherical representations of…
Induced and simple modules of double affine Hecke algebras
We classify the simple integrable modules of double affine Hecke algebras via perverse sheaves. We get also some estimate for the Jordan-Holder multiplicities of induced modules.
Fibration de Hitchin et endoscopie
We propose a geometric interpretation of the theory of elliptic endoscopy, due to Langlands and Kottwitz, in terms of the Hitchin fibration. As applications, we prove a global analog of a purity…
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