$p$-adic Hodge parameters in the crystabelline representations of ${\mathrm{G}\mathrm{L}}_3({\mathbb{Q}}_p)$

We build a one-to-one correspondence between $3$-dimensional (generic) crystabelline representations of the absolute Galois group of ${\mathbb{Q}}_p$ and certain locally analytic representations of ${\mathrm{G}\mathrm{L}}_3({\mathbb{Q}}_p)$. We show that the correspondence can be realized in subspaces of $p$-adic automorphic representations.