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Pointwise estimates of the size of characters of compact Lie groups

Part of: Abstract harmonic analysis Lie groups

Published online by Cambridge University Press:  09 April 2009

Kathryn E. Hare ,
David C. Wilson  and
Wai Ling Yee
Kathryn E. Hare
Affiliation:
Department of Pure Mathematics University of WaterlooWaterloo, OntCanada e-mail: kehare@uwaterloo.ca
David C. Wilson
Affiliation:
Po Box 280 Churchill VIC 3842Australia e-mail: davidw@utopiatype.com.au
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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 2k ∈ L1 for all central, continuous measures μ. This improves upon the known classical result which required the exponent to be dimension of the group G.

Keywords

central measurescompact Lie groupcharacters

MSC classification

Secondary: 43A80: Analysis on other specific Lie groups 22E46: Semisimple Lie groups and their representations 43A65: Representations of groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 1 , August 2000 , pp. 61 - 84
Copyright
Copyright © Australian Mathematical Society 2000

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