On the Kottwitz-Shelstad normalization of transfer factors for automorphic induction for GLn

Abstract

Automorphic induction for ${\mathrm{GL}}_n$ is a case of endoscopic transfer, and its character identity was established by Henniart and Herb, up to a constant of proportionality. We determine this constant in terms of the Kottwitz-Shelstad normalization of transfer factors, which involves certain $\epsilon$-factors.