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Finite-dimensional representations of U q (osp(1/2n)) and its connection with quantum so(2n+1)

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Abstract

It is shown that the quantum supergroup U q (osp(1/2n)) is essentially isomorphic to the quantum group U -q (so(2n+1)) restricted to tensorial representations. This renders it straightforward to classify all the finite-dimensional irreducible representations of U q (osp(1/2n)) at generic q. In particular, it is proved that at generic q, every-dimensional irrep of this quantum supergroup is a deformation of an osp(1/2n) irrep, and all the finite-dimensional representations are completely reducible.

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References

  1. KacV. G., Lecture Notes in Math. 676, 597 (1978). Scheunert, M., The Theory of Lie Superalgebras, Lecture Notes in Math. Springer-Verlag, New York, 1979.

    Google Scholar 

  2. RittenbergV. and ScheunertM., Comm. Math. Phys. 83, 1 (1982).

    Google Scholar 

  3. Drinfel'd, V. G., Quantum groups, Proc. ICM, Berkeley (1986) p. 798; Jimbo, M., Lett. Math. Phys. 10, 63 (1985).

  4. ChaichianM. and KulishP., Phys. Lett. B234, 72 (1990); Bracken, A. J., Gould, M. D., and Zhang, R. B., Modern Phys. Lett. A5, 331 (1990); Zhang, R. B., J. Math. Phys. 33, 1970 (1992). Scheunert, M., Univ. of Bonn preprint, BONN-HE-91-10; Vinet, L., et al., Univ. de Montreal preprint, UdeM-LPN-TH53 (1991).

    Google Scholar 

  5. SaleurH., Nuclear Phys. B336, 363 (1990).

    Google Scholar 

  6. ZhangR. B., BrackenA. J., and GouldM. D., Phys. Lett. B257, 133 (1991); Zhang, R. B., Gould M. D., and Bracken, A. J., J. Phys. A24, 1185 (1991).

    Google Scholar 

  7. Zachos, C. K., Paradigms of Quantum Algebras, updated version (1992).

  8. LusztigG., Adv. Math. 70, 237 (1988); Rosso, M., Comm. Math. Phys. 117, 581 (1988).

    Google Scholar 

  9. Zhang, R. B., Finite dimensional irreducible representations of the quantum supergroup U q (gl(m/n)), Australian National Univ. preprint (1991).

  10. PalevT. and TolstoyV., Comm. Math. Phys. 141, 549 (1991).

    Google Scholar 

  11. ZachosC. K., Modern Phys. Lett. 7, 1595 (1992).

    Google Scholar 

  12. FloreaniniR., SpiridonovV. P., and VinetL., Comm. Math. Phys. 137, 149 (1991); d'Hoker, E., Floreanini, R., and Vinet, L., J. Math. Phys. 32, 1427 (1991).

    Google Scholar 

  13. SchirrmacherA., WessJ., and ZuminoB., Z. Phys. C49, 317 (1991).

    Google Scholar 

Download references

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Authors and Affiliations

  1. Mathematics Research Section Institute for Advanced Studies, Australian National University, Canberra, Australia

    R. B. Zhang

  2. Department of Theoretical Physics, Institute for Advanced Studies, Australian National University, Canberra, Australia

    R. B. Zhang

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  1. R. B. Zhang
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Zhang, R.B. Finite-dimensional representations of U q (osp(1/2n)) and its connection with quantum so(2n+1). Letters in Mathematical Physics 25, 317–325 (1992). https://doi.org/10.1007/BF00398404

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  • DOI: https://doi.org/10.1007/BF00398404

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