  We study the ring of regular functions of classical spherical orbits
$R(\mathcal{O})$ for $G = Sp(2n,\mathbb{C})$. In particular, treating $G$ as a
real Lie group with maximal compact subgroup $K$, we focus on a quantization
model of $\mathcal{O}$ when $\mathcal{O}$ is the nilpotent orbit
$(2^{2p}1^{2q})$. With this model, we verify a conjecture by McGovern and
another conjecture by Achar and Sommers for such orbits. Assuming the results
in [Barbasch 2008], we will also verify the Achar-Sommers conjecture for a
larger class of nilpotent orbits.

Representation Theory