Journal of Lie Theory 16 (2006), No. 4, 743--776
Copyright Heldermann Verlag 2006
Orbital Convolution Theory for Semi-Direct Products
A. H. Dooley
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia
a.dooley@unsw.edu.au
N. J. Wildberger
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia
n.wildberger@unsw.edu.au
We extend previous results of the authors on orbital convolutions for compact groups, to compact times vector semidirect products. In particular, we define convolutions of noncompact coadjoint orbits and recover the character formulae and Plancherel formula of Lipsman.
Keywords: Lie group, semi-direct product, character formula, coadjoint orbit.
MSC: 43A80; 22E15
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