Some Results on the Locally Analytic Socle for GLn(Qp).

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 GL_n(Q_p) and show the existence of companion points for simple reflections. [ABSTRACT FROM AUTHOR]