Abstract

Bethe subalgebras form a family of maximal commutative subalgebras of the Yangian of a simple Lie algebra, parametrized by regular elements of the corresponding adjoint Lie group. We introduce an affinecrystal structure on the set of eigenlines for a Bethe subalgebra in a representation of the Yangian. This helps to describe the monodromy of solutions of Bethe ansatz for the corresponding XXX Heisenberg magnet chain. This is a joint project with Inna Mashanova-Golikova and Vasily Krylov.