# Twisted geometric Satake equivalence

@article{Finkelberg2010TwistedGS,
title={Twisted geometric Satake equivalence},
author={Michael Finkelberg and Sergey Lysenko},
journal={Journal of the Institute of Mathematics of Jussieu},
year={2010},
volume={9},
pages={719 - 739}
}
• Published 22 September 2008
• Mathematics
• Journal of the Institute of Mathematics of Jussieu
Abstract Let k be an algebraically closed field and O = k[[t]] ⊂ F = k((t)). For an almost simple algebraic group G we classify central extensions 1 → $\mathbb{G}_m\to E\to G(\bm{F})\$m → E → G(F) → 1; any such extension splits canonically over G(O). Fix a positive integer N and a primitive character ζ : μN(K) →$\mathbb{Q}}_\ell^*}$ (under some assumption on the characteristic of k). Consider the category of G(O)-bi-invariant perverse sheaves on E with $\mathbb{G}_m$m-monodromy ζ. We show that…
Quantum geometric Langlands correspondence in positive characteristic: The $\mathrm{GL}_{N}$ case
We prove a version of quantum geometric Langlands conjecture in characteristic $p$. Namely, we construct an equivalence of certain localizations of derived categories of twisted crystalline $\mathcal Twisted geometric Satake equivalence via gerbes on the factorizable grassmannian The geometric Satake equivalence of Ginzburg and Mirkovic– Vilonen, for a complex reductive group G, is a realization of the tensor category of representations of its Langlands dual group LG as a Geometric Eisenstein series: twisted setting Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on A generalized Theta lifting, CAP representations, and Arthur parameters • Spencer Leslie • Mathematics Transactions of the American Mathematical Society • 2019 We study a new lifting of automorphic representations using the theta representation$\Theta$on the$4$-fold cover of the symplectic group,$\overline{\mathrm{Sp}}_{2r}(\mathbb{A})$. This lifting Betti Geometric Langlands • Mathematics Algebraic Geometry: Salt Lake City 2015 • 2018 We introduce and survey a Betti form of the geometric Langlands conjecture, parallel to the de Rham form developed by Beilinson-Drinfeld and Arinkin-Gaitsgory, and the Dolbeault form of Twisted Satake Category We extend Bezrukavnikov and Finkelberg's description of the G(\C[[t]])-equivariant derived category on the affine Grassmannian to the twisted setting of Finkelberg and Lysenko. Our description is in Doubling Constructions and Tensor Product$L$-Functions: coverings of the symplectic group In this work we develop an integral representation for the partial$L$-function of a pair$\pi\times\tau$of genuine irreducible cuspidal automorphic representations,$\pi$of the$m\$-fold covering
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One of the fundamental results in geometric representation theory is the geometric Satake equivalence, between the category of spherical perverse sheaves on the affine Grassmannian of a reductive
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This is a translation in English of version 3 of the article arXiv:1404.3998, which is itself an introduction to arXiv:1209.5352. We explain all the ideas of the proof of the following theorem. For

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