Harmonic morphisms from the classical compact semisimple Lie groups.

<div class="Abstract"><a name="Abs1"></a><span class="AbstractHeading">Abstract  </span>In this article, we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups <a name="IEq2"></a>$${\bf SL}_n({\mathbb{R}})$$, SU *(2n), <a name="IEq1"></a>$${\bf Sp}(n, {\mathbb{R}})$$ , SO *(2n), SO(p, q), SU(p, q) and Sp(p, q) equipped with their standard dual semi-Riemannian metrics. </div> [ABSTRACT FROM AUTHOR]