Quantization of the Gaudin System
D. Talalaev
Abstract
In this article we exploit the known commutative family in Y(gl(n)) - the Bethe subalgebra - and its special limit to construct quantization of the Gaudin integrable system. We give explicit expressions for quantum hamiltonians QIk(u), k=1,..., n. At small order k=1,...,3 they coincide with the quasiclassic ones, even in the case k=4 we obtain quantum correction.
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