Unitary representations of compact quantum groups

Let v be the right regular representation of a compact quantum group G. Then ((6), Proposition 4.4) v contains all irreducible representations of G and each irreducible representation enters v with the multiplicity equal to its dimension. The result is certainly known for classical compact groups ((1)). The aim of this paper is to give a short survey on this subject and to provide a different proof of Woronowicz's result. The proof is an adaptation of the corresponding result for classical compact groups and provides a concrete decomposition of the right regular representation in irreducible components.