  Woronowicz proved the existence of the Haar state for compact quantum groups
under a separability assumption later removed by Van Daele in a new existence
proof. A minor adaptation of Van Daele's proof yields an idempotent state in
any non-empty weak*-compact convolution-closed convex subset of the state
space. Such subsets, and their associated idempotent states, are studied in the
case of quantum permutation groups.
