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On the quantum argument shift method

Sep 27, 2023
21 pages
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Abstract: (arXiv)
In a recent work by two of us the argument shift method was extended from the symmetric algebra S(g){\rm S}({\mathfrak g}) of the general linear Lie algebra g{\mathfrak g} to the universal enveloping algebra U(g){\rm 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 g{\mathfrak g}. We prove that a single application of the quasi-derivation to central elements of U(g){\rm 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 U(g){\rm U}({\mathfrak g}).
Note:
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