Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit

Abstract

In this article, we prove that the compact simple Lie groups SU(n) for n≥6, SO(n) for n≥7, Sp(n) for n≥3, E6,E7,E8, and F4 admit left-invariant Einstein metrics that are not geodesic orbit. This gives a positive answer to an open problem recently posed by Nikonorov.