  In the classification of stationary solutions in extended supergravities with
symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play
an important role. In this paper we discuss two approaches to determining the
nilpotent orbits of a real symmetric pair. We apply our methods to an explicit
example, and thereby classify the nilpotent orbits of SL_2(R)^4 acting on the
fourth tensor power of the natural 2-dimensional SL_2(R)-module. This makes it
possible to classify all stationary solutions of the so-called STU-supergravity
model.
