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

Abstract

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 $\mathrm{GL}_3(\mathbb{Q}_p)$. We show that the correspondence can be realized in subspaces of $p$-adic automorphic representations.