Local and global harmonic morphism conjecture for irreducible Riemannian symmetric spaces

Let $(M^m,g)$ be an irreducible Riemannian symmetric space of dimension $m\ge 2$. For each point $p\in M$, consider complex-valued harmonic morphisms defined on an open neighbourhood of $p$; when $(M,g)$ is of non-compact type, consider such morphisms defined on all of $M$. Harmonic morphism conjecture. For every point $p\in M$, there exists a complex-valued harmonic morphism

$$\phi:U\to\mathbb{C}$$

defined on an open neighbourhood $U$ of $p$. If $(M,g)$ is of non-compact type, the domain $U$ can be chosen to be the whole of $M$. The paper proves the conjecture except when the symmetric space is $G_2/\operatorname{SO}(4)$ or its non-compact dual.