| Résume | Building on the works of Colmez and Berger-Breuil, we determine the locally analytic vectors of the unitary representations of $GL(2,\mathbb{Q}_p)$ which correspond to (phi-semisimple) irreducible crystabelian representations of $G_{\mathbb{Q}_p}$ via the $p$-adic local Langlands correspondence of $GL(2,\mathbb{Q}_p)$. This verifies a conjecture of Breuil. |
