Analysis for idempotent states on quantum permutation groups
Operator Algebras
2025-06-26 v3 Quantum Algebra
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.
Cite
@article{arxiv.2301.13423,
title = {Analysis for idempotent states on quantum permutation groups},
author = {J. P. McCarthy},
journal= {arXiv preprint arXiv:2301.13423},
year = {2025}
}
Comments
41 pages, one figure, revised version some corrections, improvements in notation, and expanded proof by Vaes in an appendix; comments welcome via email