Bethe Subalgebras in Twisted Yangians

الأصل · EN

We study analogues of the Yangian of the Lie algebra glₙ for the other classical Lie algebras soₙ and spₙ. We call them twisted Yangians. They are coideal subalgebras in the Yangian Y(glₙ) of glₙ and admit homomorphisms onto the universal enveloping algebras U(soₙ) and U(spₙ) 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(soₙ) and U(spₙ) of these subalgebras are also maximal commutative.