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

TL;DR

This paper classifies quantum homogeneous spaces for quantum SU(2) using Tannaka-Krein duality, representing them with weighted graphs and characterizing equivariant maps through quadratic equations, especially near |q|=1.

Contribution

It extends the Tannaka-Krein duality framework to classify quantum SU(2) homogeneous spaces via weighted graphs and quadratic relations, highlighting coideal realizations near |q|=1.

Findings

Quantum homogeneous spaces are classified by weighted oriented graphs.

Equivariant maps are characterized by quadratic equations related to braiding.

All quantum homogeneous spaces are realized by coideals for |q| close to 1.

Abstract

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 the quantum SU(2) groups. We obtain a classification of their quantum homogeneous spaces in terms of weighted oriented graphs. The equivariant maps between these quantum homogeneous spaces can be characterized by certain quadratic equations associated 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.