### Abstract

We obtain positive-energy irreducible representations of the q-deformed anti de Sitter algebra U_{q}(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 (N^{2}minus;1) 2 and the Rac has dimension (N^{2}+1) 2, while if N is even both the Di and Rac have dimension N^{2} 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).

Original language | English (US) |
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Pages (from-to) | 292-298 |

Number of pages | 7 |

Journal | Physics Letters B |

Volume | 315 |

Issue number | 3-4 |

DOIs | |

State | Published - Oct 7 1993 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Physics Letters B*,

*315*(3-4), 292-298. https://doi.org/10.1016/0370-2693(93)91615-T

}

*Physics Letters B*, vol. 315, no. 3-4, pp. 292-298. https://doi.org/10.1016/0370-2693(93)91615-T

**Finite-dimensional singletons of the quantum anti de Sitter algebra.** / Dobrev, V. K.; Moylan, Patrick J.

Research output: Contribution to journal › Article

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).

UR - http://www.scopus.com/inward/record.url?scp=0006448173&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0006448173&partnerID=8YFLogxK

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 -