Nilpotent orbits in real symmetric pairs and stationary black holes. Issue 2 (20th January 2017) - Dietrich, Heiko; de Graaf, Willem A.; Ruggeri, Daniele; Trigiante, Mario
Abstract : 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 two approaches are discussed to determine the nilpotent orbits of a real symmetric pair and applied to an explicit example. Thereby the nilpotent orbits of (SL2 (R)) 4 acting on the fourth tensor power of the natural 2‐dimensional SL2 (R)‐module are clasified. This makes it possible to classify all stationary solutions of the so‐called STU‐supergravity model. Abstract : 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‐dimensional SL 2 ( R ) ‐module. This makes it possible to classify all stationary solutions of the so‐called STU‐supergravity model.