Appears in collection : Symmetry in Geometry and Analysis

Work of Kraft–Procesi classifies closures of nilpotent orbits that are normal in the cases of classical complex Lie algebras. Subsequent work of Ranee Brylinski combines this work with the Theta correspondence as defined by Howe to attach a representation of the corresponding complex group. It provides a quantization of the closure of a nilpotent orbit. In joint work with Daniel Wong we carry out a detailed analysis of these representations viewed as $(\mathfrak g, K)$-modules of the complex group viewed as a real group. One consequence is a“representation theoretic” proof of the classification of Kraft–Procesi.