Representations of the ultrahyperbolic BMS group HB. III. Determination of the representations induced from finite little groups

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. However, in studying quantum gravity, space-times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. In particular, HB, a variant of BMS group appropriate to the ultrahyperbolic signature (+,+,-,-), has been defined in a previous paper where it was shown that all the strongly continuous unitary irreducible representations (IRs) of HB can be obtained with the Wigner-Mackey's inducing method and that all the little groups of HB are compact.Here we describe in detail all the finite little groups of HB and we find all the IRs of HB induced by them.