Analysis for idempotent states on quantum permutation groups

Abstract

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.

41 pages, one figure, revised version some corrections, improvements in notation, and expanded proof by Vaes in an appendix; comments welcome via email