Notes on the BMS group in three dimensions: II. Coadjoint representation

The coadjoint representation of the BMS${}_3$ group, which governs the covariant phase space of three-dimensional asymptotically flat gravity, is investigated. In particular, we classify coadjoint BMS${}_3$ orbits and show that intrinsic angular momentum is free of supertranslation ambiguities. Finally, the link with induced representations upon geometric quantization is discussed.