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.
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P. P. Kulish and N. Yu. Reshetikhin, JETP, 53, 108–114 (1981).
P. P. Kulish and N. Yu. Reshetikhin, J. Phys. A, 16, L591–L596 (1983).
A. Varchenko and V. Tarasov, St. Petersburg Math. J., 6, 275–313 (1995).
V. Tarasov and A. Varchenko, Astérisque, 246, 1–135 (1997).
B. Enriquez, S. Khoroshkin, and S. Pakuliak, “Weight functions and Drinfeld currents,” math.QA/0610398 (2006).
V. G. Drinfeld, Sov. Math. Dokl., 36, 212–216 (1988).
B. Enriquez and V. Rubtsov, Israel J. Math., 112, 61–108 (1999).
J. Ding, S. Pakuliak, and S. Khoroshkin, Theor. Math. Phys., 124, 1007–1037 (2000).
S. Pakuliak and S. Khoroshkin, Theor. Math. Phys., 145, 1373–1399 (2005).
S. Khoroshkin, S. Pakuliak, and V. Tarasov, “Off-shell Bethe vectors and Drinfeld currents,” math.QA/0610517 (2006).
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).
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).
J. Ding, S. Khoroshkin, and S. Pakuliak, Lett. Math. Phys., 53, 121–141 (2000).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 286–303, February, 2007.
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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
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DOI: https://doi.org/10.1007/s11232-007-0018-z