Pointwise estimates of the size of characters of compact Lie groups

Source abstract

Abstract 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 L 2 . We also prove that if k = rank G then μ 2k ∈ L 1 for all central, continuous measures μ. This improves upon the known classical result which required the exponent to be dimension of the group G .