### Abstract

We obtain positive-energy irreducible representations of the q-deformed anti de Si tter algebra U_{q}(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 finite-dimensional. Generically, their dimensions are smaller than those of the corresponding finite-dimensional non-unitary representations of so(3, 2). We discuss in detail the single-ton representations, i.e. the Di and Rac. When N is odd, the Di has dimension 1/2(N^{2} - 1) and the Rac has dimension 1/2(N^{2} + 1), while if N is even, both the Di and Rac have dimension 1/2N^{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) | 171-178 |

Number of pages | 8 |

Journal | Czechoslovak Journal of Physics |

Volume | 46 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - Jan 1 1996 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Czechoslovak Journal of Physics*,

*46*(2-3), 171-178. https://doi.org/10.1007/BF01688808