Geodesic
Limits of Gaudin Systems: Classical and Quantum Cases
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the XXX homogeneous Gaudin system with $N$ sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix collide can be used to define new families of Liouville integrals (in the classical case) and new “Gaudin” algebras (in the quantum case). We will especially treat the case of total collisions, that gives rise to (a generalization of) the so called Bending flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be addressed (in the classical case). We will make use of properties of “Manin matrices” to provide explicit generators of the Gaudin Algebras in the quantum case.
Keywords: Gaudin models; Hamiltonian structures; Gaudin algebras. 
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     author = {Alexander Chervov and Gregorio Falqui and Leonid Rybnikov},
     title = {Limits of {Gaudin} {Systems:} {Classical} and {Quantum} {Cases}},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a28/}
}
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Alexander Chervov; Gregorio Falqui; Leonid Rybnikov. Limits of Gaudin Systems: Classical and Quantum Cases. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a28/

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