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Regular functions of symplectic spherical nilpotent orbits and their quantizations


Author: Kayue Daniel Wong
Journal: Represent. Theory 19 (2015), 333-346
MSC (2010): Primary 17B08, 22E10
DOI: https://doi.org/10.1090/ert/474
Published electronically: December 17, 2015
MathSciNet review: 3434893
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Abstract: 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 related to the character formula of such orbits. Assuming the results in a preprint of Barbasch, we will also verify the Achar-Sommers conjecture for a larger class of nilpotent orbits.


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Additional Information

Kayue Daniel Wong
Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Email: makywong@ust.hk

DOI: https://doi.org/10.1090/ert/474
Received by editor(s): June 13, 2015
Received by editor(s) in revised form: November 30, 2015
Published electronically: December 17, 2015
Article copyright: © Copyright 2015 American Mathematical Society