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Constructing Representations of the Nonstandardly Deformed Algebra sℓξ(2)

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Abstract

The generators of the algebra sℓξ(2), which result from the nonstandard (Jordanian) deformation of the algebra sℓ(2), are realized in the form of finite-difference operators acting in a function space. This allows realizing arbitrary-dimensional representations of sℓξ(2) in the polynomial space that are in one-to-one correspondence with usual matrices of an appropriate dimension. We discuss using the suggested realization to construct and investigate the universal R-matrix invariant with respect to the action of the algebra sℓξ(2).

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REFERENCES

  1. C. N. Yang, Phys. Rev. Lett., 19, 1312 (1967).

    Google Scholar 

  2. R. J. Baxter, Ann. Phys., 70, 193 (1972).

    Google Scholar 

  3. L. Alvarez-Gaume, C. Gomez, and G. Sierra, Phys. Lett. B, 220, 142 (1989).

    Google Scholar 

  4. N. Yu. Reshetikhin and V. G. Turaev, Comm. Math. Phys., 127, 1 (1990).

    Google Scholar 

  5. L. D. Faddeev, N. Yu. Reshetikhin, and L. A. Takhtadzhyan, “Quantization of Lie groups and Lie algebras [in Russian],” Preprint LOMI E-14-87 (1987); Leningrad Math. J., 1, 193 (1990).

    Google Scholar 

  6. V. G. Drinfel'd, “Quantum groups,” in: Proc. Intl. Congress of Mathematicians (MSRI, Berkeley, 1986), Amer. Math. Soc., Providence, R. I. (1987), p. 798; Zap. Nauchn. Sem. LOMI, 155, 18 (1986).

    Google Scholar 

  7. A. N. Kirillov and N. Yu. Reshetikhin, “Universal R-matrix for the Drinfeld–Jimbo deformation,” Preprint LOMI-E-9-88, LOMI, Leningrad (1988).

    Google Scholar 

  8. C. Ohn, Lett. Math. Phys., 25, 85 (1992).

    Google Scholar 

  9. E. E. Demidov, Yu. I. Manin, E. E. Mukhin, and D. V. Zdanovich, Progr. Theor. Phys. (Suppl.), 102, 203 (1990).

    Google Scholar 

  10. A. Aghamohammadi, M. Khorrami, and A. Shariati, J. Phys. A, 28, L225 (1995).

    Google Scholar 

  11. A. Stolin and P. P. Kulish, “New rational solutions of Yang–Baxter equation and deformed Yangians,” qalg/ 9608011 (1996); S. M. Khoroshkin, A. A. Stolin, and V. N. Tolstoy, “Deformation of Yangian Y (sl 2),” q-alg/9511005 (1995).

  12. A. Ballesteros and F. J. Herranz, J. Phys. A, 29, 4307 (1996).

    Google Scholar 

  13. L. N. Lipatov, JETPLetters, 59, 571 (1994); hep-th/9311037 (1993).

    Google Scholar 

  14. S. Derkachov, D. Karakhanyan, and R. Kirschner, Nucl. Phys. B, 583, 691 (2000); 618, 589 (2001); D. Karakhanyan, R. Kirschner, and M. Mirumyan, Nucl. Phys. B, 636, 529 (2002).

    Google Scholar 

  15. J. Van der Jeugt, “The Jordanian deformation of su(2) and Clebsch–Gordan coefficients,” q-alg/9709005 (1997).

  16. L. D. Faddeev and G. P. Korchemsky, Phys. Lett. B, 342, 311 (1995).

    Google Scholar 

  17. V. O. Tarasov, L. A. Takhtadzhyan, and L. D. Faddeev, Theor. Math. Phys., 57, 1059 (1983).

    Google Scholar 

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  1. Erevan Physics Institute, Erevan, Armenia

    D. R. Karakhanyan

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  1. D. R. Karakhanyan
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Karakhanyan, D.R. Constructing Representations of the Nonstandardly Deformed Algebra sℓξ(2). Theoretical and Mathematical Physics 138, 177–189 (2004). https://doi.org/10.1023/B:TAMP.0000014850.52009.df

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