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Geometric Weil representation: local field case

Abstract : Let k be an algebraically closed field of characteristic >2, F=k((t)) and Mp(F) denote the metaplectic extension of Sp_{2d}(F). In this paper we propose a geometric analog of the Weil representation of Mp(F). This is a category of certain perverse sheaves on some stack, on which Mp(F) acts by functors. This construction will be used in math.RT/0701170 (and subsequent publications) for a proof of the geometric Langlands functoriality for some dual reductive pairs.
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Vincent Lafforgue, Sergey Lysenko. Geometric Weil representation: local field case. Compositio Mathematica, Foundation Compositio Mathematica, 2009, 145 (01), pp.56- 88. ⟨10.1112/S0010437X08003771⟩. ⟨hal-01227218⟩

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