A local converse theorem for GL(n) (archimedean case)

TL;DR

This paper establishes a local converse theorem for GL(n) over archimedean fields, characterizing irreducible admissible representations via twisted L-factors, advancing understanding of representation theory in this setting.

Contribution

It provides the first local converse theorem for GL(n) over archimedean fields, linking representations to their twisted L-factors.

Findings

Characterization of irreducible admissible representations by twisted L-factors

Extension of local converse theorems to archimedean cases

New techniques for analyzing representations of GL(n) over R and C

Abstract

In this paper 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(R) (or GL_n(C)) in terms of twisted L-factors.