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In the study 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 determine 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‐dimensionalSL   2    (  R  )    ‐module. This makes it possible to classify all stationary solutions of the so‐called STU‐supergravity model.

Nilpotent orbits in real symmetric pairs and stationary black holes