Positive Energy Representations of the Conformal Quantum Algebra

The positive-energy unitary irreducible representations of the q-deformed conformal algebra Cq = Uq(su(2, 2)) are obtained by appropriate deformation of the classical ones. When the deformation parameter q is N -th root of unity, all these unitary representations become finitedimensional. For this case we discuss in some detail the massless representations, which are also irreducible representations of the q-deformed Poincaré subalgebra of Cq. Generically, their dimensions are smaller than the corresponding finite-dimensional non-unitary representation of su(2, 2), except when N = 2, h = 0 and N = 2|h| + 1, where h is the helicity of the representations. The latter cases include the fundamental representations with h = ±1/2. ∗ Permanent address and after 31 July 1992 : Bulgarian Academy of Sciences, Institute of Nuclear Research and Nuclear Energy, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria. ∗∗ Address after 30 September 1992 : Theoretical Physics Institute, University of Alberta, Edmonton, Canada T6G 2J1.