Let $L$ be a finite extension of $mathbb{Q}_p$ and $ngeq 2$. We associate to a crystabelline $n$-dimensional representation of $mathrm{Gal}(overline L/L)$ satisfying mild genericity assumptions a finite length locally $mathbb{Q}_p$-analytic representation of $mathrm{GL}_n(L)$. In the crystalline case and in a global context, using the recent results on the locally analytic socle from [BHS17a] we prove that this representation indeed occurs in spaces of $p$-adic automorphic forms. We then use this latter result in the ordinary case to show that certain ordinary $p$-adic Banach space representations constructed in our previous work appear in spaces of $p$-adic automorphic forms. This gives strong new evidence to our previous conjecture in the $p$-adic case.
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