Positive-energy irreps of the quantum anti de Sitter algebra (original) (raw)

1996, Czechoslovak Journal of Physics

We obtain positive-energy irreducible representations of the q-deformed anti de Sitter algebra Uq(sO(3, 2)) by deformation of the classical ones. When the deformation parameter q is N-th root of unity, all these irreducible representations become unitary and finitedimensional. Generically, their dimensions are smaller than those of the corresponding finite-dimensional non-unitary representations of so(3, 2). We discuss in detail the singleton representations, i.e. the Di and Rac. When N is odd, the Di has dimension 1 ~(N-1) and the Rac has dimension 1 2 ~(N + 1), while if N is even, both the Di and Rac have 1 2

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