The n×(n−2) local converse theorem for GL(n) over a p-adic field

In this paper, we characterize the irreducible generic representations of GL(n,F) where F is a p-adic field in terms of their γ-factors and central character. This is known as the local converse theorem. This result refines the one proved by Henniart in 1993 [G. Henniart, Caracterisation de la correspondance de Langlands locale par les facteurs ε de paires, Invent. Math. 113 (1993) 339–350].