Abstract :
For classical real Lie groups, we compute the annihilators and associated varieties of the derived functor modules cohomologically induced from the trivial representation. (Generalizing the standard terminology for complex groups, the nilpotent orbits that arise as such associated varieties are called Richardson orbits.) We show that every complex special orbit has a real form which is Richardson. As a consequence of the annihilator calculations, we give many new infinite families of simple highest weight modules with irreducible associated varieties. Finally we sketch the analogous computations for singular derived functor modules in the weakly fair range and, as an application, outline a method to detect non-normality of complex nilpotent orbit closures.
