Compositio Mathematica

Research Article

Geometric Weil representation: local field case

Vincent Lafforguea1 and Sergey Lysenkoa1

a1 Institut de Mathématiques, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France (email: vlafforg@math.jussieu.fr)

a2 Institut de Mathématiques, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France (email: lysenko@math.jussieu.fr)

Abstract

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

  • 11R39 (primary);
  • 22E50 (secondary)

Keywords

  • Weil representation;
  • metaplectic group;
  • geometric Langlands program