PreprintQuantization of the shift of argument subalgebras in type AVyacheslav Futorny and Alexander MolevAbstractGiven 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. This paper is available as a pdf (140kB) file.
