Double descent in classical groups.

Let A be the ring of adeles of a number field F. Given a self-dual irreducible, automorphic, cuspidal representation τ of GL n (A) , with a trivial central character, we construct its full inverse image under the weak Langlands functorial lift from the appropriate split classical group G. We do this by a new automorphic descent method, namely the double descent. This method is derived from the recent generalized doubling integrals of Cai, Friedberg, Ginzburg and Kaplan [CFGK17] , which represent the standard L -functions for G × GL n. Our results are valid also for double covers of symplectic groups. [ABSTRACT FROM AUTHOR]