Quantization of the Gaudin System

摘要: 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 QI_k (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.