Matrix coefficients and coadjoint orbits of compact Lie groups

Dooley, A.; Raffoul, R.

doi:10.1090/S0002-9939-07-08781-3

Matrix coefficients and coadjoint orbits of compact Lie groups
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by A. H. Dooley and R. W. Raffoul

Proc. Amer. Math. Soc. 135 (2007), 2567-2571

DOI: https://doi.org/10.1090/S0002-9939-07-08781-3

Published electronically: March 22, 2007

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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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