Bethe Subalgebras in Twisted Yangians

Details Bethe Subalgebras in Twisted Yangians Bethe Subalgebras in Twisted Yangians

1995-07-06

arxiv.org/abs/q-alg/9507003v2

Comm. Math. Phys. 178 (1996), 483-506

Mathematics

Quantum Algebra

26 pages, amstex, misprints corrected

Scientific paper

10.1007/BF02099459

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

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