Pluriclosed metrics on compact semisimple Lie groups

Abstract

Given a compact semisimple Lie group G and a maximal torus T ⊂ 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.