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}
}
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… 
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