Regular Functions of Symplectic Spherical Nilpotent Orbits and their Quantizations

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We study the ring of regular functions of classical spherical orbits R(O) for G = Sp(2n,C). In particular, treating G as a real Lie group with maximal compact subgroup K, we focus on a quantization model of O when O is the nilpotent orbit (2²ᵖ1²q). 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.