Ka Yue Wong

For a nilpotent orbit $\mathcal{O}$ in a complex classical Lie group $G$, R. Brylinski constructed a Dixmier Algebra model of its Zariski closure, based on an earlier construction by Kraft and Procesi. On the other hand, Barbasch constructed another model on $\mathcal{O}$ itself. Treating $G$ as a real Lie group with maximal compact subgroup $K$, both models can be seen as admissible $(\mathfrak{g}_{\mathbb{C}},K_{\mathbb{C}})$-modules of finite length. We are interested in finding out the composition factors of both models.