Quantum algebra U
q(2, 1): q analogs of the Gelfand-Graev formulas |
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| Authors: | Yu F Smirnov Yu I Kharitonov |
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| Institution: | (1) Institute of Nuclear Physics, Moscow State University, Moscow, Russia;(2) St. Petersburg Nuclear Physics Institute, Gatchina, Russia;(3) Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México (UNAM), México |
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| Abstract: | The discrete series of unitary irreducible representations of the noncompact quantum algebra U q(2, 1) are studied. For the negative discrete series, two bases of these irreps are considered. One of them corresponds to the reduction U q(2, 1) → U q(2)×U(1). The second basis is connected with the reduction U q(2, 1) → U(1)×U q(1, 1). The matrix elements of the U q(2, 1) generators in both bases are calculated. For the intermediate discrete series, only first type of basis is considered and the q analogs of the Gelfand-Graev formulas are obtained. Also, the transformation brackets connecting the two bases are found for the negative discrete series. |
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