Abstract
We study analogues of the Yangian of the Lie algebra\(\mathfrak{g}\mathfrak{l}_N \) for the other classical Lie algebras\(\mathfrak{s}\mathfrak{o}_N \) and\(\mathfrak{s}\mathfrak{p}_N \). We call them twisted Yangians. They are coideal subalgebras in the Yangian of\(\mathfrak{g}\mathfrak{l}_N \) and admit homomorphisms onto the universal enveloping algebras U(\(\mathfrak{s}\mathfrak{o}_N \)) and U(\(\mathfrak{s}\mathfrak{p}_N \)) respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in U(\(\mathfrak{s}\mathfrak{o}_N \)) and U(\(\mathfrak{s}\mathfrak{p}_N \)) of these subalgebras are also maximal commutative.
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Nazarov, M., Olshanski, G. Bethe subalgebras in twisted Yangians. Commun.Math. Phys. 178, 483–506 (1996). https://doi.org/10.1007/BF02099459
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DOI: https://doi.org/10.1007/BF02099459