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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Regular functions of symplectic spherical nilpotent orbits and their quantizations
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by Kayue Daniel Wong PDF
Represent. Theory 19 (2015), 333-346 Request permission

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
  • MR Author ID: 1140325
  • Email: makywong@ust.hk
  • Received by editor(s): June 13, 2015
  • Received by editor(s) in revised form: November 30, 2015
  • Published electronically: December 17, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 333-346
  • MSC (2010): Primary 17B08, 22E10
  • DOI: https://doi.org/10.1090/ert/474
  • MathSciNet review: 3434893