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A spectral theoretic approach to the Kirillov-Duflo correspondence
Author(s):
R.
W.
Raffoul
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2785-2794.
MSC (2000):
Primary 54C40, 14E20;
Secondary 46E25, 20C20
Posted:
April 6, 2009
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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  the coadjoint orbit through  , where  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:
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
Posted:
April 6, 2009
Communicated by:
Varghese Mathai
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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