The argument shift method is a simple but efficient way to produce a commutative subalgebra in a Poisson algebra, in particular in the symmetric algebra of a Lie group. Its main ingredient is an operator on the Poisson algebra that generates the elements of the commutative subalgebra by acting on its center. In my talk, I will describe an analogous operator on the universal enveloping algebra of gl(d), and show why it satisfies a similar property.