Abstract
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 ( SU q ( 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.
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