Emerton's conjecture on locally analytic vectors in unitary principal series

Let $L$ be a finite extension of ${\mathbb Q}_p$, let $\mathscr{S}_{\mathrm{irr}}$ parameterize the two-dimensional irreducible trianguline representations, and for $s=(\delta_1,\delta_2,\mathscr{L})\in\mathscr{S}_{\mathrm{irr}}$ let $V(s)$ be the associated representation and $\Sigma(s)$ the corresponding locally analytic representation. Write $\Pi(s)=\Pi(V(s))$. Emerton's conjecture. For every $s\in\mathscr{S}_{\mathrm{irr}}$, $\Pi(s)_{\mathrm{an}}$ sits in an exact sequence of locally analytic ${\mathrm{GL}}_2({\mathbb Q}_p)$-representations

$$0\longrightarrow\Sigma(s)\longrightarrow\Pi(s)_{\mathrm{an}}\longrightarrow\left({\mathrm{Ind}}^{{\mathrm{GL}}_2({\mathbb Q}_p)}_{\mathrm{B}({\mathbb Q}_p)}\delta_1\otimes\delta_2(x|x|)^{-1}\right)_{\mathrm{an}}\longrightarrow 0.$$

This conjecturally describes the locally analytic vectors in the unitary principal series representations arising from irreducible trianguline Galois representations. The paper reformulates the assertion for non-exceptional parameters in terms of the representation $\widetilde{\Sigma}(\delta_2,\delta_1)$; the general conjecture was not established in the source.