BMS modules in three dimensions

We build unitary representations of the BMS algebra and its higher-spin extensions in three dimensions, using induced representations as a guide. Our prescription naturally emerges from an ultrarelativistic limit of highest-weight representations of Virasoro and [Formula: see text] algebras, which is to be contrasted with nonrelativistic limits that typically give nonunitary representations. To support this dichotomy, we also point out that the ultrarelativistic and nonrelativistic limits of generic [Formula: see text] algebras differ in the structure of their nonlinear terms.