A local converse theorem for archimedean GL(n)

Abstract

We prove a local converse theorem for $G{L}_n$ over the archimedean local fields which characterizes an infinitesimal equivalence class of irreducible admissible representations of $G{L}_n(\mathbb{R})$ or $G{L}_n(\mathbb{C})$ in terms of twisted local gamma factors.

Accepted into Forum Mathematicum