Joint IAS/Princeton University Number Theory Seminar

**Please note: All in-person IAS seminars have been cancelled. Seminar will be livestreamed. Please follow link: https://youtu.be/vZz1SFWHiog

Recently, Cai, Friedberg, Ginzburg and Kaplan generalized the doubling method of Piatetski-Shapiro and Rallis. They found global integrals, which represent the standard L-function for pairs of irreducible, automorphic, cuspidal representations \pi - on a (split) classical group G, and \tau - on GL(n). The representation \pi need not have any particular model (such as a Whittaker model, or Bessel model, etc.). These integrals suggest an explicit descent map (an inverse to Langlands functorial lift) from GL(n) to G (appropriate G). I will show that a certain Fourier coefficient applied to a residual Eisenstein series, induced from a Speh representation, corresponding to a self-dual \tau, is equal to the direct sum of irreducible cuspidal representations \sigma \otimes \sigma', on G x G , where \sigma runs over all irreducible cuspidal representations, which lift to \tau (\sigma' is the complex conjugate of an outer conjugation of \sigma). This is a joint work with David Ginzburg.