Admissible Systems and Graded Hermitian Superspaces

We introduce the notion of admissible systems for involutions on complex contragredient Lie superalgebras, and classify the involutions with admissible systems by circlings on extended Dynkin diagrams. We prove the graded Iwasawa decomposition of the symmetric pair (g,k) consisisting of the contragredient Lie superalgebra g and the fixed points of an involution. We also show the representability in the category of complex superspaces of the corresponding real symmetric superspace.