2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63425We study G-invariant Kaehler metrics on G^C from the Hamiltonian point of view. As an application we show that there exist (GxG)-invariant Ricci-flat Kaehler metrics on G^C for any compact semisimple Lie group G.13 pages, to appear in Crelle. Statement of Theorem 1 strengthened to show existence of Kaehler metrics with arbitrary GxG-invariant Ricci form. Introduction rewritten and references added. Minor correctionsDifferential Geometry53C55; 53C25text