u
q(2,1) noncompact quantum algebra: Intermediate discrete series of unitary irreducible representations |
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| Authors: | Yu F Smirnov Yu I Kharitonov R M Asherova |
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| Institution: | (1) Petersburg Nuclear Physics Institute, Russian Academy of Sciences, Gatchina, 188350, Russia;(2) Institute of Physics and Power Engineering, pl. Bondarenko 1, Obninsk, Kaluga oblast, 249020, Russia;(3) Institute of Nuclear Physics, Moscow State University, Vorob’evy gory, Moscow, 119899, Russia |
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| Abstract: | The unitary irreducible representations of the u q(2,1) quantum algebra that belong to the intermediate discrete series are considered. The q analog of the Mickelsson-Zhelobenko algebra is developed. Use is made of the U basis corresponding to the reduction u q(2,1) ? u q(2). Explicit formulas for the matrix elements of the generators are obtained in this basis. The projection operator that projects an arbitrary vector onto the extremal vector of the intermediate-series representation is found. |
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