The Representation Ring of the Quantum Double of a Finite Group Original Research Article

We present some results about the representation ring of the quantum double of a finite group over fields of arbitrary characteristic. We give a direct sum decomposition of this representation ring into ideals involving Green rings of subgroups. Given characters of such Green rings, we construct characters of the representation ring of the quantum double and show that all characters arise in this fashion. We prove that the characters thereby obtained from Brauer characters separate modules of the quantum double up to composition factors.