We show that the minimal k such that μk ∈ L1 (SU(n)) for all central, continuous measures μ on SU(n) is k = n. We do this by exhibiting an element g ∈ SU(n) for which the (n - 1)-fold product of its conjugacy class has zero Haar measure. This ensures that if μg is the corresponding orbital measure supported on the conjugacy class, then μgn-1 is singular to L1.
|Number of pages||15|
|Journal||Israel Journal of Mathematics|
|Publication status||Published - 2002|
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