Decomposition of representations of SL(2, C) induced by the continuous series of E(2)

Abstract

Since the representations of SL(2, C) induced by irreducible unitary representations of appear as the restriction to the Lorentz group of some irreducible unitary representations of the inhomogeneous Lorentz group, the decomposition of the induced representations deserves our investigation. For the representations of SL(2, C) induced by irreducible unitary representations with discrete spin of E(2), the decomposition has been obtained by Mukunda [9]. We hope that our analysis will justify the calculations by Chakrabarti [1], [2] and [3].