Bethe subalgebras in twisted Yangians

Research paper by Maxim Nazarov, Grigori Olshanski

Indexed on: 01 May '96Published on: 01 May '96Published in: Communications in Mathematical Physics

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.