Level-raising for automorphic forms on $G{L}_n$

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 $G{L}_n({\mathbb{A}}_E)$. 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.

To appear in Transactions of the American Mathematical Society