Extensions of locally analytic generalized Steinberg representations

Abstract

Let $L$ be a finite extension of ${\mathrm{Q}}_p$. We study locally ${\mathrm{Q}}_p$-analytic generalized Steinberg representations of ${\mathrm{GL}}_n(L)$ associated with a general Zelevinsky segment and compute certain ${\mathrm{Ext}}^1$-groups involving these representations. These extension groups give rise to parabolic Breuil simple $\mathcal{L}$-invariants on the automorphic side of a conjectural $p$-adic local Langlands correspondence for potentially semistable $p$-adic Galois representations in the non-trianguline case.

arXiv comment44 pages