ABSTRACT
Real nilpotent orbits come up quite frequently in the representation theory of real Lie groups. There are two basic types of real simple Lie algebras: complex simple Lie algebras, regarded as real; and real forms of complex simple algebras. Algebras of the first type obviously yield no new nilpotent orbits, and this chapter restricts attention to real forms. The chapter presents a table of the noncompact exceptional real forms, each listed with the Cartan type of its complexified maximal compact subalgebra. It develops the theory of real nilpotent orbits. The chapter concludes by remarking that Djokovic has completely described the order relation on real classical nilpotent orbits given by containment of closures. Whenever the orbit lives in a Hermitian symmetric real form, the weighted diagram is extended so that it is a complete invariant; the additional label lies to the right of the others.
