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

Vladimir Drinfeld, Jonathan Wang

• 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.