Abstract
The Yang-Baxter operator is obtained as a product of operators that permute representation parameters in the Lax operators. The construction relies on a factorization of the Lax operator into triangular matrices. Bibliography: 13 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. D. Faddeev and L. N. Takhtajan, “The quantum method of the inverse problem and the Heisenberg XYZ model,” Russ. Math. Surv., 34, 11–68 (1979).
L. D. Faddeev, How Algebraic Bethe Ansatz Works for Integrable Model, Les-Houches Lectures (1995); hep-th/9605187.
P. P. Kulish and E. K. Sklyanin, “On the solutions of the Yang-Baxter equation,” Zap. Nauch. Semin. LOMI, 95, 129 (1980); “Quantum spectral transform method. Recent developments,” Lect. Notes Phys., 151, 61 (1982).
M. Jimbo, “Introduction to the Yang-Baxter equation,” Int. J. Mod. Phys., A 4, 3759 (1983); “Yang-Baxter equation in integrable systems,” Adv. Ser. Math. Phys., 10, M. Jimbo (ed.) World Scientific, Singapore (1990).
M. Jimbo, “A q-analogue of U(gl(n+1)), Hecke algebra, and the Yang-Baxter equation,” Lett. Math. Phys., 11, 247–252 (1986).
V. G. Drinfeld, “Hopf algebras and Yang-Baxter equation,” Sov. Math. Dokl., 32, 254 (1985); V. G. Drinfeld, “Quantum groups,” in: Proc. Int. Congress Math., Berkeley (1986), Amer. Math. Soc. (1987), p. 798.
P. P. Kulish, N. Yu. Reshetikhin, and E. K. Sklyanin, “Yang-Baxter equation and representation theory,” Lett. Math. Phys., 5, 393–403 (1981).
S. Derkachov and A. Manashov, “R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain,” SIGMA, 2:084 (2006); nlin.si/0612003.
S. Derkachov and A. Manashov, “Baxter operators for the quantum sl(3) invariant spin chain,” J. Phys. A, 39, 13171 (2006); nlin.si/0604018.
S. Derkachov, D. Karakhanyan, and R. Kirschner, “Yang-Baxter R-operators and parameter permutations,” Nucl. Phys., B785, 263–285 (2007); hep-th/0703076.
A. Klimyk and K. Schmudgen, Quantum Groups and Their Representations, Texts and Monographs in Physics, Springer (1997).
L. C. Biedenharn and M. A. Lohe, Quantum Group Symmetry and q-Tensor Algebras, World Scientific, Singapore (1995); L. C. Biedenharn and M. A. Lohe, Comm. Math. Phys., 146, 483–504 (1992).
L. D. Faddeev and R. M. Kashaev, “Quantum dilogarithm,” Mod. Phys. Lett. A, 9, 427 (1994); A. N. Kirillov, “Dilogarithm identities,” Progr. Theor. Phys. Suppl., 118, 61–142 (1995); hep-th/9408113; A. Yu. Volkov, “Noncommutative hypergeometry,” math.QA/0312084.
Author information
Authors and Affiliations
Additional information
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 88–106.
Rights and permissions
About this article
Cite this article
Valinevich, P.A., Derkachov, S.E., Karakhanyan, D. et al. Factorization of the \( \mathcal{R} \)-matrix for the quantum algebra U q (sℓ3). J Math Sci 151, 2848–2858 (2008). https://doi.org/10.1007/s10958-008-9005-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-008-9005-7