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Discrete series of unitary irreducible representations of the U q (u(3, 1)) and U q (u(n, 1)) noncompact quantum algebras

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Abstract

The structure of all discrete series of unitary irreducible representations of the U q (u(3, 1)) and U q (u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g′) q . The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U q (u(n, 1)) ⊇ U q (u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) ⊇ u(n) classical algebra.

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Authors and Affiliations

  1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991, Russia

    Yu. F. Smirnov & R. M. Asherova

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  1. Yu. F. Smirnov
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  2. R. M. Asherova
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Correspondence to R. M. Asherova.

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Original Russian Text © Yu.F. Smirnov, R.M. Asherova, 2011, published in Yadernaya Fizika, 2011, Vol. 74, No. 6, pp. 836–850.

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Smirnov, Y.F., Asherova, R.M. Discrete series of unitary irreducible representations of the U q (u(3, 1)) and U q (u(n, 1)) noncompact quantum algebras. Phys. Atom. Nuclei 74, 808–823 (2011). https://doi.org/10.1134/S1063778811060275

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  • DOI: https://doi.org/10.1134/S1063778811060275

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