Pointwise estimates of the size of characters of compact Lie groups

Kathryn E. Hare, David C. Wilson, Wai Ling Yee
2000 Journal of the Australian Mathematical Society  
Pointwise bounds for characters of representations of the classical, compact, connected, simple Lie groups are obtained 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 L 2 . We also prove that if k = rank G then /i 2 * e L x for all central, continuous measures \i. This improves upon the known classical result which required the exponent to be the dimension
more » ... be the dimension of the group G. 2000 Mathematics subject classification: primary 43A80; secondary 22E46,43A65.
doi:10.1017/s1446788700001841 fatcat:d25n23qhzze5bbnk6lqixuqfdq