On the existence of harmonic morphisms from certain symmetric spaces

In this paper we give a positive answer to the open existence problem for complex-valued harmonic morphisms from the non-compact irreducible Riemannian symmetric spaces SLn(R)/SO(n), SU∗(2n)/Sp(n) and their compact duals SU(n)/SO(n) and SU(2n)/Sp(n). Furthermore we prove the existence of globally defined, complex-valued harmonic morphisms from any Riemannian symmetric space of type IV.