Geometric Weil representation: local field case

Vincent Lafforgue (1) , Sergey Lysenko (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Géométrie

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.

Domaines: Théorie des représentations [math.RT]

Vincent Lafforgue, Sergey Lysenko. Geometric Weil representation: local field case. Compositio Mathematica, 2009, 145 (01), pp.56- 88. ⟨10.1112/S0010437X08003771⟩. ⟨hal-01227218⟩