Harmonic morphisms from the compact semisimple Lie groups and their non-compact duals

In this paper we prove the local existence of complex-valued harmonic morphisms from any compact semisimple Lie group and their non-compact duals. These include all Riemannian symmetric spaces of types II and IV. We produce a variety of concrete harmonic morphisms from the classical compact simple Lie groups SO(n), SU(n), Sp(n) and globally defined solutions on their non-compact duals SO(n, C)/SO(n), SLn (C)/SU(n) and Sp(n, C)/Sp(n). (c) 2005 Elsevier B.V. All rights reserved.