Consider a compact quantum group G. Let a, b and c be irreducible unitary corepresentations and assume that c is contained in a \otimes b. Let U be the intertwiner from the representation Hilbert space of c to the one of a \otimes b and assume that U is a partial isometry. By Schur his lemma U is determined up to a phase factor.

Question: Can we assume that U has real (Clebsch-Gordan) coefficients?  

If not, is there a good class of examples for which this is true? Or is it true for free orthogonal/unitary QG's?