Geometric Weil representation: local field case

摘要

Let k be an algebraically closed field of characteristic greater than 2, and let F = k((t)) and G = Sp_(2d). In this paper we propose a geometric analog of the Weil representation of the metaplectic group G(F). This is a category of certain perverse sheaves on some stack, on which G(F) acts by functors. This construction will be used by Lysenko (in [Geometric theta-lifting for the dual pair SO_(2m), Sp_(2n) math.RT/0701170] and subsequent publications) for the proof of the geometric Langlands func toriality for some dual reductive pairs.