Construction of the Bethe State for the $\mathrm E_{\tau,\eta}(so_3)$ Elliptic Quantum Group
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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Elliptic quantum groups can be associated to solutions of the star-triangle relation of statistical mechanics. In this paper, we consider the particular case of the $E_{\tau,\eta}(so_3)$ elliptic quantum group. In the context of algebraic Bethe ansatz, we construct the corresponding Bethe creation operator for the transfer matrix defined in an arbitrary representation of $E_{\tau,\eta}(so_3)$.
Keywords: elliptic quantum group; algebraic Bethe ansatz.
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Nenad Manojlović; Zoltán Nagy. Construction of the Bethe State for the $\mathrm E_{\tau,\eta}(so_3)$ Elliptic Quantum Group. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a3/

[1] Avan J., Babelon O., Billey E., “The Gervais–Neveu–Felder equation and the quantum Calogero–Moser system”, Comm. Math. Phys., 178 (1996), 281–300 | DOI | MR

[2] Billey E., Algebraic nested Bethe ansatz for the elliptic Ruijsenaars model, math.QA/9806068

[3] Faddeev L. D., “How algebraic Bethe ansatz works for integrable models”, Symétries quantiques, Proceedings of the “Les Houches Summer School, Session LXIV” (1 August–8 September, 1995, Les Houches, France), eds. A. Connes, K. Gawedzki and J. Zinn-Justin, North-Holland, Amsterdam, 1998, 149–219 ; hep-th/9605187 | MR | Zbl

[4] Felder G., Conformal field theory and integrable systems associated to elliptic curves, hep-th/9407154 | MR

[5] Felder G., Varchenko A., “Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau,\eta}(sl_2)$”, Nuclear Phys. B, 480 (1996), 485–503 ; q-alg/9605024 | DOI | MR | Zbl

[6] Felder G., Varchenko A., “Elliptic quantum groups and Ruijsenaars models”, J. Statist. Phys., 89 (1997), 963–980 ; q-alg/9704005 | DOI | MR | Zbl

[7] Felder G., Varchenko A., “On representations of the elliptic quantum group $E_{\tau,\eta}(sl_2)$”, Comm. Math. Phys., 181 (1996), 741–761 ; q-alg/9601003 | DOI | MR | Zbl

[8] Hou B. Y., Sasaki R., Yang W.-L., “Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau,\eta}(sl_n)$ and its applications”, Nuclear Phys. B, 663 (2003), 467–486 ; hep-th/0303077 | DOI | MR | Zbl

[9] Jimbo M., Miwa T., Okado M., “Solvable lattice models related to the vector representation of classical simple Lie algebras”, Comm. Math. Phys., 116 (1988), 507–525 | DOI | MR | Zbl

[10] Korepin V. E., Boguliubov N. M., Izergin A. G., Quantum inverse scattering method and correlation functions, Cambridge Monograph on Mathematical Physics, Cambridge University Press, 1993 | MR | Zbl

[11] Kulish P. P., Sklyanin E. K., Quantum spectral transform method. Recent developments, Lecture Notes in Phys., 151, eds. J. Hietarinta and C. Montonen, Springer, New York, 1982, 61–119 | MR

[12] Manojlović N., Nagy Z., “Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau,\eta}(so_3)$”, J. Math. Phys., 48:12 (2007), 123515, 11 pp. | DOI | MR | Zbl

[13] Tarasov V. O., “Algebraic Bethe ansatz for the Izergin–Korepin $R$-matrix”, Theoret. and Math. Phys., 76:2 (1988), 793–803 | DOI | MR