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Finite-dimensional representations of the quantum superalgebraU q[gl(n/m)] and relatedq-identities

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Abstract

Explicit expressions for the generators of the quantum superalgebraU q [gl(n/m)] acting on a class of irreducible representations are given. The class under consideration consists of all essentially typical representations: for these a Gel'fand-Zetlin basis is known. The verification of the quantum superalgebra relations to be satisfied is shown to reduce to a set ofq-number identities.

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Author notes

  1. T. D. Palev & N. I. Stoilova

    Present address: Institute for Nuclear Research and Nuclear Energy, 1784, Sofia, Bulgaria

Authors and Affiliations

  1. International Centre for Theoretical Physics, I-34100, Trieste, Italy

    T. D. Palev

  2. Department of Applied Mathematics and Computer Science, University of Ghent, Krijgslaan 281-S9, B-9000, Gent, Belgium

    T. D. Palev, N. I. Stoilova & J. Van der Jeugt (Research Associate of the N.F.W.O. (National Fund for Scientific Research of Belgium)

Authors
  1. T. D. Palev
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  2. N. I. Stoilova
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  3. J. Van der Jeugt
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Communicated by M. Jimbo

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Palev, T.D., Stoilova, N.I. & Van der Jeugt, J. Finite-dimensional representations of the quantum superalgebraU q[gl(n/m)] and relatedq-identities. Commun.Math. Phys. 166, 367–378 (1994). https://doi.org/10.1007/BF02112320

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  • DOI: https://doi.org/10.1007/BF02112320

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