On a strange invariant bilinear form on the space of automorphic forms

• Vladimir Drinfeld ^[1] ; Jonathan Wang ^[1]
  1. [1] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 4 (Special Issue: The Mathematics of Joseph Bernstein), 2016, págs. 1825-1880
• Idioma: inglés
• DOI: 10.1007/s00029-016-0262-x
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• Resumen

  • Let F be a global field and G := SL(2). We study the bilinear form B on the space of K-finite smooth compactly supported functions on G(A)/G(F) defined by B( f1, f2) := Bnaive( f1, f2) − M−1 CT( f1) ,CT( f2), where Bnaive is the usual scalar product, CT is the constant term operator, and M is the standard intertwiner. This form is natural from the viewpoint of the geometric Langlands program. To justify this claim, we provide a dictionary between the classical and ‘geometric’ theory of automorphic forms. We also show that the form B is related to S. Schieder’s Picard–Lefschetz oscillators.