TY - JOUR

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

AU - Dobrev, V. K.

AU - Moylan, P. J.

N1 - Funding Information:
V.K.D. would like to thank Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality and financial support at the ICTP. V.K.D. was also partially supported by the Bulgarian National Foundation for Science, Grant ~-11.

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 -