Multiplicity one theorems for the generalized doubling method

In this work we prove the local multiplicity at most one theorem underlying the definition and theory of local $γ$-, $ε$- 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.

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