Quasi-admissible, raisable nilpotent orbits, and theta representations

We study the quasi-admissibility and raisablility of some nilpotent orbits of a covering group. In particular, we determine the degree of the cover such that a given split nilpotent orbit is quasi-admissible and non-raisable. The speculated wavefront sets of theta representations are also computed explicitly, and are shown to be quasi-admissible and non-raisable. Lastly, we determine the leading coefficients in the Harish-Chandra character expansion of theta representations of covers of the general linear groups.