Some results on locally analytic socle for $\mathrm{GL}_n(\mathbb{Q}_p)$

Abstract

We study some closed rigid subspaces of the eigenvarieties, constructed by using the Jacquet-Emerton functor for parabolic non-Borel subgroups. As an application (and motivation), we prove some new results on Breuil's locally analytic socle conjecture for $\mathrm{GL}_n(\mathbb{Q}_p)$.