C(SO_q(4)/SO_q(2)) is isomorphic to C*(G_tight) for the tight groupoid from the classical inverse semigroup, with four locally closed orbits whose isotropy groups are Z, inducing four families of irreps parametrized by T equivalent to Soibelman ones.
and Saurabh B., Topological Invariance of Quantum Homogeneous Spaces of Type B and D
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$C(SO_q(4)/SO_q(2))$ as a Groupoid $C^*$-algebra
C(SO_q(4)/SO_q(2)) is isomorphic to C*(G_tight) for the tight groupoid from the classical inverse semigroup, with four locally closed orbits whose isotropy groups are Z, inducing four families of irreps parametrized by T equivalent to Soibelman ones.