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Infinite Dimensional Representations of Quantum Algebras

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Symmetries in Science VI
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Abstract

Quantum groups and algebras are of great importance for different branches of physics and mathematics. In order to apply them in theoretical and mathematical physics one has to develop the theory of representations of these groups and algebras.

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References

  1. M. Rosso, Commum. Math. Phys., 117: 581–593 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. M. Jimbo, Lect. Notes Phys., 146: 334–361 (1986).

    Google Scholar 

  3. V.K. Dobrev, in: “Symmetries in Science V”, B. Gruber, L.C. Biedenharn and H.D. Doebner, eds., Plenum, New York, (1991).

    Google Scholar 

  4. G. Lusztig, Adv. Math., 70: 237–249 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  5. A.U. Klimyk, “Matrix Elements and Clebsch-Gordan Coefficients of Group Representations, Naukova Dumka, Kiev, (1979).

    Google Scholar 

  6. L. Vaksman and L. Korogodsky, Preprint ITP-90-27P, Kiev, (1989).

    Google Scholar 

  7. A.U. Klimyk and V.A. Groza, Preprint ITP-89-37P, Kiev, (1989).

    Google Scholar 

  8. A.U. Klimyk, Preprint ITP-89-37P, Kiev, (1989).

    Google Scholar 

  9. A. Chakrabarti, Preprint, Paris, (1990).

    Google Scholar 

  10. A.U. Klimyk, Yu.F. Smirnov and B. Gruber, in: “Symmetries in Science V”, B. Gruber, L.C. Biedenharn and H.D. Doebner, eds., Plenum, New York, (1991).

    Google Scholar 

  11. V,A. Groza, I.I. Kachurik and A.U. Klimyk, J. Math. Phys., 31: 2769–2780 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi and K. Ueno, C. R. Akad. Sci. Paris, Ser. Math., 307: 559–564 (1988); J. Funct. Anal., 99: 357-386 (1991).

    MathSciNet  MATH  Google Scholar 

  13. T.H. Koornwinder, Nederl. Akad. Vetensch. Proc., Ser. A, 92: 97–117 (1989).

    MathSciNet  Google Scholar 

  14. L. Vaksman and Y. Soibelman, Funct Anal Appl., 22: 170–174 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  15. T. Masuda, K. Mimachi, Y. Nakagami, M. Noumi, Y. Saburi and K. Ueno, “Representations of the Quantum Group SU q,(1, 1): I & II”, Preprints, (1989).

    Google Scholar 

  16. N. Noumi and K. Mimachi, Commun. Math. Phys., 128: 521–531 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. G. Gasper and M. Rahman, “Basic Hypergeometric Functions”, Cambridge Univ. Press, Cambridge, (1990).

    Google Scholar 

  18. M. Jimbo, Lett. Math. Phys., 10: 63–69 (1985).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. A.U. Klimyk and S. Pakuliak, J. Math. Phys., 33: (1992).

    Google Scholar 

  20. A.U. Klimyk and B. Gruber, J. Math. Phys., 20: 2011–2013 (1979).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. A.U. Klimyk and B. Gruber, J. Math. Phys., 23: 1399–1408 (1982).

    Article  MathSciNet  ADS  MATH  Google Scholar 

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© 1993 Springer Science+Business Media New York

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Klimyk, A.U., Pakuliak, S. (1993). Infinite Dimensional Representations of Quantum Algebras. In: Gruber, B. (eds) Symmetries in Science VI. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1219-0_33

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  • DOI: https://doi.org/10.1007/978-1-4899-1219-0_33

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1221-3

  • Online ISBN: 978-1-4899-1219-0

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