Tannaka-Krein duality for compact quantum homogeneous spaces. II. Classification of quantum homogeneous spaces for quantum SU(2)

摘要

We apply the Tannaka-Krein duality theory for quantum homogeneous spaces,developed in the first part of this series of papers, to the case of thequantum SU(2) groups. We obtain a classification of their quantum homogeneousspaces in terms of weighted oriented graphs. The equivariant maps between thesequantum homogeneous spaces can be characterized by certain quadratic equationsassociated with the braiding on the representations of SUq(2). We show that,for |q| close to 1, all quantum homogeneous spaces are realized by coideals.