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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the quantization of spherical nilpotent orbits
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by Liang Yang PDF
Trans. Amer. Math. Soc. 365 (2013), 6499-6515 Request permission

Abstract:

Let $G$ be the real symplectic group $Sp(2n,\mathbb {R})$. This paper determines the global sections of certain line bundles over the spherical nilpotent $K_{\mathbb {C}}$-orbit $\mathcal {O}$. As a consequence, Vogan’s conjecture for these orbits is verified. The conjecture holds that there exists a unique unitary $(\mathfrak {g},K)$-module structure on the space of the algebraic global sections of the line bundle associated to the admissible datum, provided that the boundary $\partial \overline {\mathcal {O}}$ has complex codimension at least $2$ in $\overline {\mathcal {O}}$. Similar results are obtained for the metaplectic twofold cover $Mp(2n,\mathbb {R})$ of $Sp(2n,\mathbb {R})$.
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Additional Information
  • Liang Yang
  • Affiliation: Department of Mathematics, Sichuan University, Chengdu, 610064, People’s Republic of China
  • Email: malyang@scu.edu.cn
  • Received by editor(s): November 9, 2011
  • Received by editor(s) in revised form: May 20, 2012
  • Published electronically: April 25, 2013
  • Additional Notes: Part of this work was included in the author’s Ph.D. thesis
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 6499-6515
  • MSC (2010): Primary 20G15, 22E46
  • DOI: https://doi.org/10.1090/S0002-9947-2013-05925-9
  • MathSciNet review: 3105760