Electric-magnetic duality in twisted quantum double model of topological orders

We derive a partial electric-magnetic (PEM) duality transformation of the twisted quantum double (TQD) model TQD(G, alpha) - discrete Dijkgraaf-Witten model - with a finite gauge group G, which has an Abelian normal subgroup N , and a three-cocycle alpha is an element of H-3(G, U(1)). Any equivalence between two TQD models, say, TQD(G, alpha) and TQD(G ', alpha '), can be realized as a PEM duality transformation, which exchanges the N-charges and N-fluxes only. Via the PEM duality, we construct an explicit isomorphism between the corresponding TQD algebras D-alpha(G) and D-alpha '(G ') and derive the map between the anyons of one model and those of the other.