The gl_2 Bethe algebra associated with a nilpotent element
  To any 2x2-matrix K one assigns a commutative subalgebra B^{K}\subset U(gl_2[t]) called a Bethe algebra. We describe relations between the Bethe algebras, associated with the zero matrix and a nilpotent matrix. 
E. Mukhin, V. Tarasov, A. Varchenko