a1 Institut de Mathématiques, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France (email: [email protected])
a2 Institut de Mathématiques, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France (email: [email protected])
Let k be an algebraically closed field of characteristic greater than 2, and let F=k((t)) and G=𝕊p2d. In this paper we propose a geometric analog of the Weil representation of the metaplectic group . This is a category of certain perverse sheaves on some stack, on which acts by functors. This construction will be used by Lysenko (in [Geometric theta-lifting for the dual pair S𝕆2m, 𝕊p2n, math.RT/0701170] and subsequent publications) for the proof of the geometric Langlands functoriality for some dual reductive pairs.
(Received June 26 2007)
(Accepted April 16 2008)
2000 Mathematics Subject Classification