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

 

A spectral theoretic approach to the Kirillov-Duflo correspondence


Author: R. W. Raffoul
Journal: Proc. Amer. Math. Soc. 137 (2009), 2785-2794
MSC (2000): Primary 54C40, 14E20; Secondary 46E25, 20C20
Published electronically: April 6, 2009
MathSciNet review: 2497493
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09916-X
PII: S 0002-9939(09)09916-X
Keywords: Lie groups, coadjoint orbits
Received by editor(s): August 13, 2008
Published electronically: April 6, 2009
Communicated by: Varghese Mathai
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.