## A spectral theoretic approach to the Kirillov-Duflo correspondence

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**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.## References

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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