Reduced Solutions of Toda Systems for Arbitrary Complex Simple Lie Algebras

Abstract

We study reduced solutions of Toda systems generated by spherical metrics for an arbitrary complex simple Lie algebra. The main result is an intrinsic centralizer parametrization: for a spherical metric, the reduced family is the positive Iwasawa slice cut out by the centralizer of the principal image of closure of monodromy group. As an application, we transfer existing spherical-metric existence results to the diagonal Toda source tuple.