Compact quantum ergodic systems

We develop theory of multiplicity maps for compact quantum groups. As an application, we obtain a complete classification of right coideal C∗-algebras of C(SUq(2)) for q∈[−1,1)∖{0}. They are labeled with Dynkin diagrams, but classification results for positive and negative cases of q are different. Many of the coideals are quantum spheres or quotient spaces by quantum subgroups, but we do have other ones in our classification list.