SEPARATION OF VARIABLES AND THE XXZ GAUDIN MAGNET(11)

Abstract. In this work we generalise previous results connecting (rational) Gaudin magnet models and classical separation of variables. It is shown that the connection persists for the case of linear r-matrix algebra which corresponds to the trigonometric

SEPARATION OF VARIABLES AND THE XXZ GAUDIN MAGNET

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1. E.G

. Kalnins, Separation of Variables for Riemannian Spaces of Constant Curvature, Pitman Monographs and Surveys in Pure and Applied Mathematics 28, Longman Scienti c and Technical, Essex, England, 1986. 2. E.G. Kalnins and W.Miller Jr., Separation of variables on n-dimensional Riemannian manifolds.1.The n-sphere Sn and Euclidean n-space Rn, J. Math. Phys. 27 (1986), 1721. 3. E.G. Kalnins, W. Miller Jr. and G.J. Reid, Separation of variables for complex Riemannian spaces of constant curvature 1. Orthogonal separable coordinates for coordinates SnC and EnC, Proc. Roy. Soc. Lond. A394 (1984), 183. 4. E.K. Sklyanin, Separation of variables in the Gaudin model, J. Sov. Math. 47 (1989), 2473. 5. I.V. Komarov and V.B. Kuznetsov, Quantum Euler-Manakov top on the 3-sphere S3, J. Phys. A: Math. Gen. 24 (1991), L737. 6. V.B. Kuznetsov, Equivalence of two graphical calculi, J. Phys. A: Math. Gen. 25 (1992), 6005. 7. V.B. Kuznetsov, Quadrics on real Riemannian spaces of constant curvature. Separation of variables and connection with Gaudin magnet, J. Math. Phys. 33 (1992), 3240. 8. E.G. Kalnins, V.B. Kuznetsov and W. Miller, Quadrics on complex Riemannian spaces of constant curvature, separation of variables and the Gaudin magnet, J. Math. Phys. 35 (1994), 1710. 9. M. Gaudin, La fonction d onde de Bethe, Masson, Paris, 1983. 10. L.D. Faddeev and L.A. Takhtajan, Hamiltonian Methods in the Theory of Solitons, Springer, Berlin, 1987. 11. A.G. Reyman and M.A. Semenov-Tian-Shansky, Group-theoretic methods in the theory of integrable systems, In: Encyclopedia of Mathematical Sciences, Dynamical Systems 7, volume 16, Springer, Berlin, 1994. 12. E.K. Sklyanin, On the Poisson structure of the periodic classical XYZ-chain, J. Sov. Math. 46 (1989), 1664.0

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