Functional calculus and coadjoint orbits.

Download files
Access & Terms of Use
open access
Copyright: Raffoul, Raed Wissam
Abstract
Let G be a compact Lie group and let π be an irreducible representation of G of highest weight λ. We study the operator-valued Fourier transform of the product of the j-function and the pull-back of ð by the exponential mapping. We show that the set of extremal points of the convex hull of the support of this distribution is the coadjoint orbit through ë + ä. The singular support is furthermore the union of the coadjoint orbits through ë + wä, as w runs through the Weyl group. Our methods involve the Weyl functional calculus for noncommuting operators, the Nelson algebra of operants and the geometry of the moment set for a Lie group representation. In particular, we re-obtain the Kirillov-Duflo correspondence for compact Lie groups, independently of character formulae. We also develop a "noncommutative" version of the Kirillov character formula, valid for noncentral trigonometric polynomials. This generalises work of Cazzaniga, 1992.
Persistent link to this record
Link to Publisher Version
Additional Link
Author(s)
Raffoul, Raed Wissam
Supervisor(s)
Creator(s)
Editor(s)
Translator(s)
Curator(s)
Designer(s)
Arranger(s)
Composer(s)
Recordist(s)
Conference Proceedings Editor(s)
Other Contributor(s)
Corporate/Industry Contributor(s)
Publication Year
2007
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
Files
download whole.pdf 466.48 KB Adobe Portable Document Format
Related dataset(s)