On the quantum argument shift method

Abstract

In a recent work by two of us the argument shift method was extended from the symmetric algebra $\mathrm{S}(\mathfrak{g})$ of the general linear Lie algebra $\mathfrak{g}$ to the universal enveloping algebra $\mathrm{U}(\mathfrak{g})$. We show in this paper that some features of this 'quantum argument shift method' can be applied to the remaining classical matrix Lie algebras $\mathfrak{g}$. We prove that a single application of the quasi-derivation to central elements of $\mathrm{U}(\mathfrak{g})$ yields elements of the corresponding quantum Mishchenko-Fomenko subalgebra. We show that generators of this subalgebra can be obtained by iterated application of the quasi-derivation to generators of the center of $\mathrm{U}(\mathfrak{g})$.

arXiv comment21 pages

References in corpus (6)

• Gaudin models with irregular singularities
• Bethe Subalgebras in Twisted Yangians
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• Braided Weyl algebras and differential calculus on U(u(2))
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• On Segal--Sugawara vectors and Casimir elements for classical Lie algebras