Limits of Gaudin systems: classical and quantum cases

@article{Chervov2009LimitsOG,
  title={Limits of Gaudin systems: classical and quantum cases},
  author={Alexander Chervov and Gregorio Falqui and Leonid Rybnikov},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2009},
  volume={5},
  pages={029}
}
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… Expand

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