  The original Bondi-Metzner-Sachs (BMS) group B is the common asymptotic
symmetry group of all asymptotically flat Lorentzian radiating 4-dim
space-times. As such, B is the best candidate for the universal symmetry group
of General Relativity (G.R.). In 1973, with this motivation, P. J. McCarthy
classified all relativistic B-invariant-systems in terms of strongly continuous
irreducible unitary repesentations (IRS) of B. Here we introduce the analogue
B(2,1) of the BMS group B in 3 space-time dimensions. B(2,1) itself admits
thirty-four analogues both real in all signatures and in complex space-times.
In order to find the IRS of both B(2,1) and its analogues we need to extend
Wigner-Mackey's theory of induced representations. The necessary extension is
described and is reduced to the solution of three problems. These problems are
solved in the case where B(2,1) and its analogues are equipped with the Hilbert
topology. The extended theory is necessary in order to construct the IRS of
both B and its analogues in any number d of space-time dimensions, d is greater
or equal to 3, and also in order to construct the IRS of their supersymmetric
counterparts. We use the extended theory to obtain the necessary data in order
to construct the IRS of B(2,1): The main results of the representation theory
are: The IRS are induced from little groups which are compact. The finite
little groups are cyclic groups of even order. The inducing construction is
exhaustive notwithstanding the fact that B(2,1) is not locally compact in the
employed Hilbert topology.
