Admissible positive systems of affine Kac–Moody Lie algebras: The twisted cases

We introduce admissible positive systems and Hermitian real forms of affine twisted Kac–Moody Lie algebras, and show that a real form has admissible positive system if and only if it is Hermitian. We use the Vogan diagrams to classify the Hermitian real forms, and show that their symmetric spaces carry complex structures. The affine non-twisted Kac–Moody Lie algebras have been treated in an earlier work, and this article deals with the twisted cases.