Abstract
Using the Functional Bethe Ansatz technique, factorizing Drinfel'd twists for any finite dimensional irreducible representations of the Yangian Y(sl2) are constructed.
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Chari, V. and Pressley, A.: Yangians and R-matrices, Enseign. Math. 36 (1990) 267–302.
Drinfel'd, V. G.: On constant, quasiclassical solutions of the Yang–Baxter quantum equation, Soviet Math. Dokl. 28(3) (1983), 667–671.
Drinfeld, V. G.: Hopf algebras and the quantum Yang–Baxter equation, Soviet Math. Dokl. 32(1) (1985), 254–258.
Drinfel'd, V. G.: Quantum groups, In: Proc. Internat. Congress of Math., Berkeley, U.S.A., 1986, 1987, pp. 798–820.
Drinfel'd, V. G.: Quasi-Hopf algebras, Leningrad Math. J. 1(6) (1990), 1419–57.
Freidel, L. and Maillet, J.-M.: The Universal R-matrix and its associated Quantum Algebra as functionals of the Classical r-matrix: the sl 2 case, Phys. Lett. B 296 (1992), 353–360.
Jimbo, M.: A q-difference analogue of U(g) and the Yang–Baxter equation, Lett. Math. Phys. 10 (1985), 63–69.
Jimbo, M.: A q-analogue of U(gl(N + 1)), Hecke algebra, and the Yang–Baxter equation, Lett. Math. Phys. 11 (1986), 247–252.
Khoroshkin, S. and Tolstoy, V.: Yangian double, Lett. Math. Phys. 36 (1996), 373–402.
Kitanine, N., Maillet, J.M. and Terras, V.: Form factors of the XXZ Heisenberg spin-1/2 finite chain 1998, to appear in Nuclear Phys. B, math-ph/9807020.
Maillet, J.M. and Sanchez de Santos, J.: Drinfel'd twists and algebraic Bethe ansatz, 1996, q-alg/9612012.
Sklyanin, E. K.: Functional Bethe Ansatz. In: B. Kupershmidt (ed.): Integrable and Superintegrable Systems, World Scientific, Singapore, 1990, pp. 8–33.
Sklyanin, E. K.: Quantum inverse scattering method. Selected topics, In: M.-L. Ge (ed.): Quantum Group and Quantum Integrable Systems, 1992, pp. 63–97.
Tarasov, V.: Irreducible monodromy matrices for the R-matrix of the XXZ model and local lattice quantum Hamiltonians, Theor. Math. Phys. 63(2) (1985), 440–454.
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Terras, V. Drinfel'd Twists and Functional Bethe Ansatz. Letters in Mathematical Physics 48, 263–276 (1999). https://doi.org/10.1023/A:1007695001683
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DOI: https://doi.org/10.1023/A:1007695001683