Level-raising for automorphic forms on $GL_n$

TL;DR

This paper proves a level-raising theorem for automorphic representations on $GL_n$ over CM fields, extending previous results by relaxing key assumptions such as ramification conditions and field restrictions.

Contribution

It generalizes existing level-raising results for automorphic forms on $GL_n$ by removing several restrictive hypotheses, allowing broader applicability.

Findings

Level-raising prime $p$ can be unramified, not just inert.

Applicable to general CM fields without assuming $E/F$ is everywhere unramified.

Extends Thorne's results to more general settings.

Abstract

Let $E$ be a CM number field and $F$ its maximal real subfield. We prove a level-raising result for regular algebraic conjugate self-dual automorphic representations of $GL_n(\mathbb{A}_E)$. This generalizes previously known results of Thorne by removing certain hypotheses occurring in that work. In particular, the level-raising prime $p$ is allowed to be unramified as opposed to inert in $F$, the field $E/F$ is not assumed to be everywhere unramified, and the field $E$ is allowed to be a general CM field.