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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Matrix coefficients and coadjoint orbits of compact Lie groups


Authors: A. H. Dooley and R. W. Raffoul
Journal: Proc. Amer. Math. Soc. 135 (2007), 2567-2571
MSC (2000): Primary 43A77, 22E99; Secondary 47Nxx
Published electronically: March 22, 2007
MathSciNet review: 2302577
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08781-3
PII: S 0002-9939(07)08781-3
Keywords: Coadjoint orbits, Lie groups, matrix coefficients, moment map, Weyl functional calculus.
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
Article copyright: © Copyright 2007 American Mathematical Society