Extensions of locally analytic generalized parabolic Steinberg representations

TL;DR

This paper investigates the structure and extensions of locally analytic generalized parabolic Steinberg representations of GL_n over p-adic fields, connecting them to Breuil's invariants and the p-adic Langlands program.

Contribution

It computes Ext-groups for these representations and explores their relation to Breuil's simple invariants within the p-adic Langlands framework.

Findings

Computed Ext-groups of the representations.

Linked the representations to Breuil's simple invariants.

Provided insights into the automorphic aspects of p-adic Langlands.

Abstract

Let $L$ be a finite extension of $\mathbf{Q}_p$. In this paper, we study the locally $\mathbf{Q}_p$-analytic generalized parabolic Steinberg representations of $\mathrm{GL}_n(L)$, and compute the $\mathrm{Ext}$-groups of locally $\mathbf{Q}_p$-analytic generalized parabolic Steinberg representations. They carry the Breuil's simple $\mathcal{L}$-invariants, which arise in the automorphic side of a conjectured $p$-adic local Langlands correspondence.