Resumen de On the extended Whittaker category

Dario Beraldo

• Let G be a connected reductive group with connected center and X a smooth complete curve, both defined over an algebraically closed field of characteristic zero. Let BunG denote the stack of G-bundles on X. In analogy with the classical theory of Whittaker coefficients for automorphic functions, we construct a “Fourier transform” functor coeffG,ext from the DG category of D -modules on BunG to a certain DG category Wh(G,ext) , called the extended Whittaker category. This construction allows to formulate the compatibility of the Langlands duality functor LG:IndCohN(LocSysGˇ)→D(BunG) with the Whittaker model. For G=GLn and G=PGLn , we prove that coeffG,ext is fully faithful. This result guarantees that, for those groups, LG is unique (if it exists) and necessarily fully faithful.