A local converse theorem for archimedean GL(n)

TL;DR

This paper establishes a local converse theorem for archimedean fields, characterizing irreducible admissible representations of GL(n) over real and complex numbers via twisted gamma factors, advancing understanding in representation theory.

Contribution

It provides a new characterization of irreducible admissible representations of GL(n) over archimedean fields using gamma factors, filling a gap in the local Langlands correspondence.

Findings

Characterization of representations via gamma factors

Extension of local converse theorems to archimedean fields

Enhanced understanding of representation equivalence classes

Abstract

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