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Australasian Research Symposium on Lie Groups, Algebraic Groups, Quantum Groups, and Their Representations (LAQ'2001)
December 7-10, 2001
The University of Auckland
Auckland, New Zealand

Organizers
Rod Gover (University of Auckland), Vladimir Pestov (Victoria University of Wellington)

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Orbital convolution theory for semi-direct products
by
A.H. Dooley
UNSW

The idea that one can understand convolution of central distributions on a Lie group by studying Euclidean convolution of Ad-invariant distributions on the Lie algebra leads to new insights into the Kirillov character formula. Some years ago, Norm Wildberger and I showed that for compact Lie groups, this theory actually holds in a global sense: in our version, there is no restriction on the supports of the Ad-invariant distributions. Recently we have extended our theory to compact times vector semi-direct products. This is technically interesting as the adjoint orbits are no longer compact. We can produce a full analogue of the compact case, and prove a version of Lipsman's character formlua.

Date received: October 31, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahw-18.