### 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) |
---|---|

Pages (from-to) | 292-298 |

Number of pages | 7 |

Journal | Physics Letters B |

Volume | 315 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Oct 7 1993 |

### Fingerprint

### 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