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Bethe subalgebras in twisted Yangians

Authors:	Maxim Nazarov Grigori Olshanski

Institution:	(1) University of Wales, SA2 8PP Swansea, UK;(2) Institute for Problems of Information Transmission, 101447 Moscow, Russia

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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