Limits of Gaudin Systems: Classical and Quantum Cases - Mathematics > Quantum AlgebraReport as inadecuate




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Abstract: We consider the XXX homogeneous Gaudin system with $N$ sites, both inclassical and the quantum case.
In particular we show that a suitable limitingprocedure for letting the poles of its Lax matrix collide can be used to definenew families of Liouville integrals in the classical case and new -Gaudin-algebras in the quantum case.
We will especially treat the case of totalcollisions, that gives rise to a generalization of the so called Bendingflows of Kapovich and Millson.
Some aspects of multi-Poisson geometry will beaddressed in the classical case.
We will make use of properties of -Maninmatrices- to provide explicit generators of the Gaudin Algebras in the quantumcase.



Author: Alexander Chervov, Gregorio Falqui, Leonid Rybnikov

Source: https://arxiv.org/



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