Level-raising for automorphic forms on 𝐺𝐿_{𝑛}

Abstract

Let E E be a CM number field and F F its maximal real subfield. We prove a level-raising result for regular algebraic conjugate self-dual automorphic representations of G L n ( A E ) GL_{n}(\mathbb {A}_E) . This generalizes previously known results of Thorne [Forum Math. Sigma 2 (2014)] by removing certain hypotheses occurring in that work. In particular, the level-raising prime p p is allowed to be unramified as opposed to inert in F F , the field E / F E/F is not assumed to be everywhere unramified, and the field E E is allowed to be a general CM field.