Спектры подалгебр Бете в ЯнгианахSpectra of Bethe subalgebras in Yangians

Yangians and Bethe subalgebras were introduced by V. Drinfeld and are used in studying the XXX Heisenberg chain. The image of Bethe subalgebra $B(C)$ in a tensor product of evaluation representations of $Y(\fgl_n)$ form a complete set of Hamiltonians of the XXX Heisenberg magnet chain. The main problem in the XXX integrable system is the diagonalization of the subalgebras $B(C)$ in the corresponding representation of the Yangian. The standard approach is the algebraic Bethe ansatz. The questions we address in our work are closely related to the completeness of the algebraic Bethe ansatz. As the first step towards the solution of this problem, it is necessary that the joint eigenvalues have no multiplicities. In our work we discuss some new results on the simplicity of spectra of Bethe subalgebras in several new cases including tame representations of the Yangian in type A with generic values of the parameters and some "small" Kirillov-Reshetikhin modules in other types.