Global uniqueness of small representations

TL;DR

This paper proves that automorphic representations with specific small local components are unique in their multiplicity, using a new multiplicity-one theorem for small representations.

Contribution

It introduces a new multiplicity-one theorem for small representations and applies it to establish global uniqueness of certain automorphic representations.

Findings

Automorphic representations with small local components have multiplicity one.

A new multiplicity-one theorem for small representations is established.

The proof links local properties to global uniqueness results.

Abstract

We prove that automorphic representations whose local components are certain small representations have multiplicity one. The proof is based on the multiplicity-one theorem for certain functionals of small representations, also proved in this paper.