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The original Bondi-Metzner-Sachs (BMS) group B is the common asymptoticsymmetry group of all asymptotically flat Lorentzian radiating 4-dimspace-times. As such, B is the best candidate for the universal symmetry groupof General Relativity (G.R.). In 1973, with this motivation, P. J. McCarthyclassified all relativistic B-invariant-systems in terms of strongly continuousirreducible unitary repesentations (IRS) of B. Here we introduce the analogueB(2,1) of the BMS group B in 3 space-time dimensions. B(2,1) itself admitsthirty-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 extendWigner-Mackey's theory of induced representations. The necessary extension isdescribed and is reduced to the solution of three problems. These problems aresolved in the case where B(2,1) and its analogues are equipped with the Hilberttopology. The extended theory is necessary in order to construct the IRS ofboth B and its analogues in any number d of space-time dimensions, d is greateror equal to 3, and also in order to construct the IRS of their supersymmetriccounterparts. We use the extended theory to obtain the necessary data in orderto construct the IRS of B(2,1): The main results of the representation theoryare: The IRS are induced from little groups which are compact. The finitelittle groups are cyclic groups of even order. The inducing construction isexhaustive notwithstanding the fact that B(2,1) is not locally compact in theemployed Hilbert topology.

On the representation theory of the Bondi-Metzner-Sachs group and its variants in three space-time dimensions