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

Abstract

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 ) , SL n ( C ) / SU ( n ) and Sp ( n , C ) / Sp ( n ) .