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Geometric Weil representation: local field case

  • Vincent Lafforgue (a1) and Sergey Lysenko (a1)
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.

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References
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[1]Drinfeld, B., Quantization of the Hitchin integrable system and Hecke eigensheaves, Preprint, downloadable from http://www.math.utexas.edu/∼benzvi/Langlands.html.
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[9]Lysenko, S., Moduli of metaplectic bundles on curves and theta-sheaves, Ann. Sci. École Norm. Sup. (4) 39 (2006), 415466.
[10]Lysenko, S., Geometric theta-lifting for the dual pair S𝕆2m,𝕊p2n, math.RT/0701170.
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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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