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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A spectral theoretic approach to the Kirillov-Duflo correspondence
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by R. W. Raffoul PDF
Proc. Amer. Math. Soc. 137 (2009), 2785-2794 Request permission

Abstract:

The Kirillov-Duflo orbit correspondance for compact Lie groups is parametrisation of the unitary dual, associating to the irreducible representation of highest weight $\lambda$ the coadjoint orbit through $\lambda +\delta$, where $\delta$ is half the sum of the positive roots and justified by the character formulae of Weyl or Kirillov. In this paper we obtain this correspondence independently of character theory, showing that it arises from a convexity property of the Weyl functional calculus of the infinitesimal generators of the representation.
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Additional Information
  • R. W. Raffoul
  • Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
  • Email: raed@maths.unsw.edu.au
  • Received by editor(s): August 13, 2008
  • Published electronically: April 6, 2009
  • Communicated by: Varghese Mathai
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2785-2794
  • MSC (2000): Primary 54C40, 14E20; Secondary 46E25, 20C20
  • DOI: https://doi.org/10.1090/S0002-9939-09-09916-X
  • MathSciNet review: 2497493