TY - JOUR

T1 - Finite-dimensional singletons of the quantum anti de Sitter algebra

AU - Dobrev, V. K.

AU - Moylan, Patrick J.

PY - 1993/10/7

Y1 - 1993/10/7

N2 - 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 an Nth root of unity, all these irreducible representations become unitary and finite-dimensional. Generically, their dimensions are smaller than of the corresponding finite-dimensional non-unitary representation 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 (N2minus;1) 2 and the Rac has dimension (N2+1) 2, while if N is even both the Di and Rac have dimension N2 2. These dimensions are classical only for N=3 when the Di and Rac are deformations of the two fundamental non-unitary representations of so(3,2).

AB - 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 an Nth root of unity, all these irreducible representations become unitary and finite-dimensional. Generically, their dimensions are smaller than of the corresponding finite-dimensional non-unitary representation 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 (N2minus;1) 2 and the Rac has dimension (N2+1) 2, while if N is even both the Di and Rac have dimension N2 2. These dimensions are classical only for N=3 when the Di and Rac are deformations of the two fundamental non-unitary representations of so(3,2).

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U2 - 10.1016/0370-2693(93)91615-T

DO - 10.1016/0370-2693(93)91615-T

M3 - Article

AN - SCOPUS:0006448173

VL - 315

SP - 292

EP - 298

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3-4

ER -