Admissible positive systems of affine non-twisted Kac-Moody Lie algebras

We introduce admissible positive systems and Hermitian real forms of affine non-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.