The size of characters of compact Lie groups

Kathryn E. Hare

ArticleOriginal scientific text

Title

The size of characters of compact Lie groups

Authors ¹

Affiliations

Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Abstract

Pointwise upper bounds for characters of compact, connected, simple Lie groups are obtained which enable one to prove that if μ is any central, continuous measure and n exceeds half the dimension of the Lie group, then

μ^{n} \in L^{1}

. When μ is a continuous, orbital measure then

μ^{n}

is seen to belong to

L^{2}

. Lower bounds on the p-norms of characters are also obtained, and are used to show that, as in the abelian case, m-fold products of Sidon sets are not p-Sidon if p < 2m/(m+1).

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Title

The size of characters of compact Lie groups

Affiliations

Abstract

Bibliography