Pluriclosed metrics on compact semisimple Lie groups

Abstract

Given a compact semisimple Lie group G and a maximal torus T of G, we give an explicit description of all left and Ad(T)-invariant pluriclosed Hermitian structures on G in terms of the corresponding root system. They depend on 2d+1 parameters in the irreducible case, where dim(T)=2d. As applications, we obtain that the only left and Ad(T)-invariant pluriclosed metrics which are also CYT are bi-invariant metrics (i.e., Bismut flat) and study the pluriclosed flow as a neat ODE system.