On the irreducibility of locally analytic principal series representations

Let $\mathbf{G}$ be a $p$-adic connected reductive group with Lie algebra $\mathfrak{g}$. For a parabolic subgroup $\mathbf{P} \subset \mathbf{G}$ and a finite-dimensional locally analytic representation $V$ of a Levi subgroup of $\mathbf{P}$, we study the induced locally analytic $\mathbf{G}$-representation $W = \operatorname{Ind}_{\mathbf{P}}^{\mathbf{G}}(V)$. Our result is the following criterion concerning the topological irreducibility of $W$: If the Verma module $U(\mathfrak{g}) \otimes_{U(\mathfrak{p})} V'$ associated to the dual representation $V'$ is irreducible, then $W$ is topologically irreducible as well.