Quantization of the Gaudin System

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 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.

9 pages

References in corpus (3)

• Bethe Subalgebras in Twisted Yangians
• Rational Lax operators and their quantization
• Yangians and their applications

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