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

TL;DR

This paper investigates the structure of eigenvarieties related to n(p)) and advances understanding of Breuil's locally analytic socle conjecture through new theoretical results.

Contribution

It introduces new methods for analyzing eigenvarieties and proves novel results on Breuil's conjecture for n(p)).

Findings

Construction of closed rigid subspaces of eigenvarieties.

New results supporting Breuil's locally analytic socle conjecture.

Enhanced understanding of the representation theory of n(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 $\mathrm{GL}_n(\mathbb{Q}_p)$.