Affine Poisson Groups and WZW Model
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a detailed description of a dynamical system which enjoys a Poisson–Lie symmetry with two non-isomorphic dual groups. The system is obtained by taking the $q\to\infty$ limit of the $q$-deformed WZW model and the understanding of its symmetry structure results in uncovering an interesting duality of its exchange relations.
Keywords: Poisson–Lie symmetry; WZW model.
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Ctirad Klimcík. Affine Poisson Groups and WZW Model. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a2/

[1] Chu M., Goddard P., Halliday I., Olive D., Schwimmer A., “Quantization of the Wess–Zumino–Witten model on a circle”, Phys. Lett. B, 266 (1991), 71–81 | DOI | MR | Zbl

[2] Dazord P., Sondaz D., “Groupes de Poisson affines”, Symplectic Geometry, Groupoids, and Integrable Systems (1989, Berkeley, CA), Math. Sci. Res. Inst. Publ., 20, eds. P. Dazord and A. Weinstein, Springer, New York, 1991, 99–128 | MR

[3] Dorfman I. Ya., “Deformations of Hamiltonian structures and integrable systems”, Proceedings of Second International Workshop on Nonlinear and Turbulent Processes in Physics, Vol. 3 (October 19–25, 1983, Kyiv), ed. R. Z. Sagdeev, Harwood Academic Publishers, 1984, 1313–1318 | MR

[4] Felder G., “Conformal field theory and integrable systems associatedto elliptic curves”, Proceedings of the International Congress of Mathematicians (1994, Zürich), Birkhäuser, Basel, 1995, 1247–1255 ; hep-th/9407154 | MR | Zbl

[5] Klimčík C., “Quasitriangular WZW model”, Rev. Math. Phys., 16 (2004), 679–808 ; hep-th/0103118 | DOI | MR | Zbl

[6] Klimčík C., “$q\to\infty$ limit of the quasitriangular WZW model”, J. Nonlinear Math. Phys., 14 (2007), 486–518 ; math-ph/0611066 | DOI | MR

[7] Koszul J. L., “Crochet de Schouten–Nijenhuis et cohomologie”, Astérisque, 137, 1985, 257–271 | MR

[8] Lu J.-H., Multiplicative and affine Poisson structures on Lie groups, Ph.D. Thesis, University of California, Berkeley, 1990; available at http://hkumath.hku.hk/~jhlu/publications.html

[9] Lukyanov S., Shatashvili S., “Free field representation for the classical limit of quantum affine algebra”, Phys. Lett. B, 298 (1993), 111–115 ; hep-th/9209130 | DOI | MR

[10] Magri F., Morosi C., A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson–Nijenhuis manifolds, Quaderno, 19, University of Milano, 1984

[11] Reshetikhin N. Yu., Semenov-Tian-Shansky M. A., “Central extensions of quantum current groups”, Lett. Math. Phys., 19 (1990), 133–142 | DOI | MR | Zbl