J. Aust. Math. Soc.  77 (2004), 233-248
The size of characters of exceptional Lie groups

Kathryn E. Hare
  Department of Pure Mathematics
  University of Waterloo
  Waterloo, Ont. N2L 3G1
  Canada
  kehare@uwaterloo.ca
and
Karen Yeats
  Department of Pure Mathematics
  University of Waterloo
  Waterloo, Ont. N2L 3G1
  Canada
  kayeats@uwaterloo.ca


Abstract
Pointwise bounds for characters of representations of the compact, connected, simple, exceptional Lie groups are obtained. It is a classical result that if $\mu$ is a central, continuous measure on such a group, then $\mu^{\dim G}$ is absolutely continuous. Our estimates on the size of characters allow us to prove that the exponent, dimension of $G$, can be replaced by approximately the rank of $G$. Similar results were obtained earlier for the classical, compact Lie groups.
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