On a local conjecture of Jacquet, ladder representations and standard modules

Abstract

Let $E/F$ be a quadratic extension of p-adic fields. We prove that every smooth irreducible ladder representation of the group $G{L}_n(E)$ which is contragredient to its own Galois conjugate, possesses the expected distinction properties relative to the subgroup $G{L}_n(F)$. This affirms a conjecture attributed to Jacquet for a large class of representations. Along the way, we prove a reformulation of the conjecture which concerns standard modules in place of irreducible representations.

arXiv comment21 pages, to appear in Mathematische Zeitschrift