Given a simple Lie algebra $\mathfrak{ g}$ and an element $\mu\in\mathfrak{ g}^*$, the corresponding shift of argument subalgebra of $\text{ S}(\mathfrak{ g})$ is Poisson commutative. In the case where $\mu$ is regular, this subalgebra is known to admit a quantization, that is, it can be lifted to a commutative subalgebra of $\text{ U}(\mathfrak{ g})$. We show that if $\mathfrak{ g}$ is of type $A$, then this property extends to arbitrary $\mu$, thus proving a conjecture of Feigin, Frenkel and Toledano Laredo. The proof relies on an explicit construction of generators of the center of the affine vertex algebra at the critical level.
Categories: math.RT