Multiplicity one theorems for the generalized doubling method (with an appendix by Avraham Aizenbud and Dmitry Gourevitch)

Abstract

We prove the local multiplicity at most one theorem underlying the definition and theory of local $\gamma$-, $ϵ$- and $L$-factors, defined by virtue of the generalized doubling method, over any local field of characteristic 0. We also present two applications: one to the existence of local factors for genuine representations of covering groups, the other to the global unfolding argument of the doubling integral.