J Austral Math Soc Ser A 56 pp64--116, 1994.

On the Fourier Transform of a Compact Semisimple Lie Group

N. J. Wildberger

Abstract

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 occuring 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.

1991 AMS Subject Classification: 22E46, 58F06

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Authors

N. J. Wildberger

Department of Pure Mathematics, University of N.S.W. P.O. Box 1, Kensington, N.S.W 2033, Australia.