Black Hole Nilpotent Orbits and Tits Satake Universality Classes

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In this paper we consider the problem of classification of nilpotent orbits for the pseudo-quaternionic coset manifolds U/H* obtained in the time-like dimensional reduction of N = 2 supergravity models based on homogeneous symmetric special geometries.

• Within the D=3 approach this classification amounts to a classification of regular and singular extremal black hole solutions of supergravity.
• We show that the pattern of such orbits is a universal property depending only on the Tits-Satake universality class of the considered model, the number of such classes being five.
• We present a new algorithm for the classification and construction of the nilpotent orbits for each universality class which is based on an essential use of the Weyl group W of the Tits Satake subalgebra U_{TS} of U and on a certain subgroup W_H thereof.