Pluriclosed metrics on compact semisimple Lie groups

TL;DR

This paper characterizes all invariant pluriclosed Hermitian structures on compact semisimple Lie groups, revealing their parameter dependence, identifying CYT metrics as bi-invariant, and analyzing the pluriclosed flow through an ODE system.

Contribution

It provides an explicit classification of invariant pluriclosed structures on compact semisimple Lie groups and explores their properties and evolution.

Findings

Invariant pluriclosed structures depend on 2d+1 parameters.

The only invariant pluriclosed CYT metrics are bi-invariant.

The pluriclosed flow reduces to a simple ODE system.

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.