ASYMPTOTIC SYMMETRIES IN 3-DIM GENERAL RELATIVITY: THE B(2,1) CASE

Abstract

The ordinary Bondi—Metzner—Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space—times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). Strongly continuous unitary irreducible representations (IRs) of B(2, 1), the analogue of B in three space—time dimensions, are analysed in the Hilbert topology. It is proved that all IRs of B(2, 1) are induced from IRs of compact ‘little groups’, which are the closed subgroups of SO(2). It is proved that all IRs of B(2, 1) are obtained by Wigner—Mackey’s inducing construction notwithstanding the fact that B(2, 1) is not locally compact in the employed Hilbert topology.