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Pointwise estimates of the size of characters of compact Lie groups

Published online by Cambridge University Press:  09 April 2009

Kathryn E. Hare
Affiliation:
Department of Pure Mathematics University of WaterlooWaterloo, OntCanada e-mail: [email protected]
David C. Wilson
Affiliation:
Po Box 280 Churchill VIC 3842Australia e-mail: [email protected]
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Abstract

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Pointwise bounds for characters of representations of the classical, compact, connected, simple Lie groups are obtained with which allow us to study the singularity of central measures. For example, we find the minimal integer k such that any continuous orbital measure convolved with itself k times belongs to L2. We also prove that if k = rank G then μ 2kL1 for all central, continuous measures μ. This improves upon the known classical result which required the exponent to be dimension of the group G.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

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