On the Fourier Transform of a Compact Semisimple Lie Group

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 occurring inner products on Them. A global Kirillov-type character is obtained for each irreducible Representation. The case of St/(2) is Treated in some detail, where some interesting connections with classical spherical Trigonometry are obtained. © 1994, Australian Mathematical Society. All rights reserved.