Скачать или смотреть David Soudry (Tel Aviv University): Double descent for classical groups

Talk on Nov 4 on the WIS Representation theory and Algebraic Geometry seminar.

Abstract: We consider thegeneralized doubling integrals of Cai, Friedberg, Ginzburg and Kaplan. These generalize the doubling method of Piatetski-Shapiro and Rallis andrepresent the standard L-function for pairs of irreducible, automorphic,cuspidal representations \pi - on a (split) classical group G, and \tau - onGL(n). The representation \pi need not have any particular model (such as a Whittaker model, or a Bessel model). 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 aresidual Eisenstein series, induced from a Speh representation, corresponding toa self-dual \tau, is equal to the direct sum of irreducible cuspidal representations \sigma \otimes \sigma', on G x G , where \sigma runs over allirreducible 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.

Slides:

https://www.dropbox.com/s/u0o1gar0gly...