  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.
