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New boson representations of the sl q (2) with multiplicity two and new solutions to the Yang-Baxter equation atq p=1

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Abstract

Whenq is a root of unity, the representations of the quantum universal enveloping algebra sl q (2) with multiplicity two are constructed from theq-deformed boson realization with an arbitrary parameter which is in a very general form and is first presented in this Letter. The new solutions to the Yang-Baxter equation are obtained from these representations through the universalR-matrix.

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References

  1. Drinfeld, V. G., Quantum groups, inProc. 1986 IMC, Amer. Math. Soc., Berkeley, 1987, p. 798.

  2. Jimbo, M.,Lett. Math. Phys. 10, 63 (1985);11, 247 (1986).

    Article  Google Scholar 

  3. Reshetikhin, N. Yu., LOMI preprint E4, E11 1988.

  4. Lusztig, G.,Adv. Math. 70, 237 (1988);Contemp. Math. 82, 59 (1989).

    Article  Google Scholar 

  5. Rosso, R.,Comm. Math. Phys. 117, 581 (1988);124, 307 (1989).

    Article  Google Scholar 

  6. Roche, P. and Arnaudon, D.,Lett. Math. Phys. 17, 295 (1989).

    Article  Google Scholar 

  7. Pasguier, V. and Suler, H.,Nuclear Phys. B330, 523 (1990).

    Google Scholar 

  8. Sun, C. P., Lu, J. F., and Ge, M. L.,J. Phys. A24, (1991) in press.

  9. Biedenharn, L. C.,J. Phys. A22, L873 (1989).

  10. Sun, C. P. and Fu, H. C.,J. Phys. A22, L983 (1989).

  11. Macfarlane, A. J.,J. Phys. A22, 4551 (1989).

    Google Scholar 

  12. Sun, C. P. and Ge, M. L.,J. Math. Phys. 34, (1991) in press.

  13. Sun, C. P. and Ge, M. L.,q-deformed boson representations of quantum algebras withq p=1, (I) and (II), preprints.

  14. Sun, C. P., Liu, X. F., and Ge, M. L., A newq-deformed boson realization of the quantum algebra sl q (n) and its representations, to appear inJ. Math. Phys.

  15. Date, E., Jimbo, M., Miki, K., and Miwa, T.,Phys. Lett. A 148, 45 (1990).

    Google Scholar 

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Authors and Affiliations

  1. Theoretical Physics Division, Nankai Institute of Mathematics, 300071, Tianjin, P.R. China

    Mo-Lin Ge, Xu-Feng Liu & Chang-Pu Sun

  2. Physics Department, Northeast Normal University, 130024, Changchun, P.R. China

    Chang-Pu Sun

Authors
  1. Mo-Lin Ge
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  2. Xu-Feng Liu
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  3. Chang-Pu Sun
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Additional information

This work is supported in part by the National Foundation of Natural Science of China.

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Ge, ML., Liu, XF. & Sun, CP. New boson representations of the sl q (2) with multiplicity two and new solutions to the Yang-Baxter equation atq p=1. Lett Math Phys 23, 169–178 (1991). https://doi.org/10.1007/BF01885495

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  • DOI: https://doi.org/10.1007/BF01885495

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