J. Aust. Math. Soc. 77 (2004), 233–248 THE SIZE OF CHARACTERS OF EXCEPTIONAL LIE GROUPS

Pointwise bounds for characters of representations of the compact, connected, simple, exceptional Lie groups are obtained. It is a classical result that if is a central, continuous measure on such a group, then dimG 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