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Geometric Weil representation: local field case

Part of: Algebraic number theory: global fields Lie groups

Published online by Cambridge University Press:  01 January 2009

Vincent Lafforgue  and
Sergey Lysenko
Vincent Lafforgue
Affiliation:
Institut de Mathématiques, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France (email: vlafforg@math.jussieu.fr)
Sergey Lysenko
Affiliation:
Institut de Mathématiques, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France (email: vlafforg@math.jussieu.fr)
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Abstract

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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 $\widetilde G(F)$. This is a category of certain perverse sheaves on some stack, on which $\widetilde G(F)$ 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.

Keywords

Weil representationmetaplectic groupgeometric Langlands program

MSC classification

Secondary: 11R39: Langlands-Weil conjectures, nonabelian class field theory 22E50: Representations of Lie and linear algebraic groups over local fields

Information

Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 1 , January 2009 , pp. 56 - 88
Copyright
Copyright © Foundation Compositio Mathematica 2009

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