Satake superdiagrams, real forms and Iwasawa decomposition of classical Lie superalgebras

Satake superdiagrams corresponding to the Lie superalgebras , , , C(n), together with the exceptional ones are constructed from their Dynkin diagrams with a view to determine the real forms of these superalgebras. The involutive automorphisms are computed from a modified formula to account for all pertinent cases in a consistent way. This mechanism is also used to furnish a general treatment of the Iwasawa and Langlands decompositions of these superalgebras. In particular, we compute these decompositions for for illustrational purposes and obtain the corresponding induced representations using the method of Schmidt construction.