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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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Matrix coefficients and coadjoint orbits of compact Lie groups
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by A. H. Dooley and R. W. Raffoul PDF
Proc. Amer. Math. Soc. 135 (2007), 2567-2571 Request permission

Abstract:

Let $G$ be a compact Lie group. We use Weyl functional calculus (Anderson, 1969) and symplectic convexity theorems to determine the support and singular support of the operator-valued Fourier transform of the product of the $j$-function and the pull-back of an arbitrary unitary irreducible representation of $G$ to the Lie algebra, strengthening and generalizing the results of Cazzaniga, 1992. We obtain as a consequence a new demonstration of the Kirillov correspondence for compact Lie groups.
References
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Additional Information
  • A. H. Dooley
  • Affiliation: School of Mathematics, University of New South Wales, Sydney NSW 2000, Australia
  • Email: a.dooley@unsw.edu.au
  • R. W. Raffoul
  • Affiliation: School of Mathematics, University of New South Wales, Sydney NSW 2000, Australia
  • Email: raed@maths.unsw.edu.au
  • Received by editor(s): April 18, 2006
  • Published electronically: March 22, 2007
  • Additional Notes: The authors gratefully acknowledge the support of the Australian Research Council.
  • Communicated by: Jane M. Hawkins
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2567-2571
  • MSC (2000): Primary 43A77, 22E99; Secondary 47Nxx
  • DOI: https://doi.org/10.1090/S0002-9939-07-08781-3
  • MathSciNet review: 2302577