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On the Fourier transform of a compact semisimple Lie group

Part of: Lie groups

Published online by Cambridge University Press:  09 April 2009

N. J. Wildberger
N. J. Wildberger
Affiliation:
Department of Pure Mathematics, University of N. S. W.. P. O. Box 1, Kensington N. S. W.2033, Australia
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Abstract

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We develop a concrete Fourier transform on a compact Lie group by means of a symbol calculus, or *-product, on each integral co-adjoint orbit. These *-products are constructed by means of a moment map defined for each irreducible representation. We derive integral formulae for these algebra structures and discuss the relationship between two naturally occurring inner products on them. A global Kirillov-type character is obtained for each irreducible representation. The case of SU(2) is treated in some detail, where some interesting connections with classical spherical trigonometry are obtained.

MSC classification

Secondary: 22E46: Semisimple Lie groups and their representations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 1 , February 1994 , pp. 64 - 116
Copyright
Copyright © Australian Mathematical Society 1994

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