Skip to main content
Log in

Projection method and a universal weight function for the quantum affine algebra

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We calculate the projection of the product of the Drinfeld currents on the intersection of the different Borel subalgebras in the current realization of the quantum affine algebra

. This projection yields a universal weight function and has the structure of nested Bethe vectors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. P. Kulish and N. Yu. Reshetikhin, JETP, 53, 108–114 (1981).

    Google Scholar 

  2. P. P. Kulish and N. Yu. Reshetikhin, J. Phys. A, 16, L591–L596 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  3. A. Varchenko and V. Tarasov, St. Petersburg Math. J., 6, 275–313 (1995).

    MathSciNet  Google Scholar 

  4. V. Tarasov and A. Varchenko, Astérisque, 246, 1–135 (1997).

    Google Scholar 

  5. B. Enriquez, S. Khoroshkin, and S. Pakuliak, “Weight functions and Drinfeld currents,” math.QA/0610398 (2006).

  6. V. G. Drinfeld, Sov. Math. Dokl., 36, 212–216 (1988).

    MathSciNet  Google Scholar 

  7. B. Enriquez and V. Rubtsov, Israel J. Math., 112, 61–108 (1999).

    MathSciNet  Google Scholar 

  8. J. Ding, S. Pakuliak, and S. Khoroshkin, Theor. Math. Phys., 124, 1007–1037 (2000).

    Article  MATH  Google Scholar 

  9. S. Pakuliak and S. Khoroshkin, Theor. Math. Phys., 145, 1373–1399 (2005).

    Article  Google Scholar 

  10. S. Khoroshkin, S. Pakuliak, and V. Tarasov, “Off-shell Bethe vectors and Drinfeld currents,” math.QA/0610517 (2006).

  11. V. G. Drinfeld, “Quantum groups,” in: Proc. Intl. Congress of Mathematicians (Berkeley, CA, August 3–11, 1986, A. M. Gleason, ed.), Amer. Math. Soc., Providence, R. I. (1987), pp. 798–820; M. Jimbo, Lett. Math. Phys., 10, 63–69 (1985).

    Google Scholar 

  12. S. Khoroshkin and V. N. Tolstoy, “Twisting of quantum (super)algebras: Connection of Drinfeld’s and Cartan-Weyl realizations for quantum affine algebras,” Preprint MPIM1994-23, Max-Planck-Inst. Math., Bonn (1994); hep-th/9404036 (1994).

    Google Scholar 

  13. J. Ding, S. Khoroshkin, and S. Pakuliak, Lett. Math. Phys., 53, 121–141 (2000).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 286–303, February, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pakuliak, S.Z., Khoroshkin, S.M. Projection method and a universal weight function for the quantum affine algebra . Theor Math Phys 150, 244–258 (2007). https://doi.org/10.1007/s11232-007-0018-z

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-007-0018-z

Keywords

Navigation