Quantization of the shift of argument subalgebras in type A

摘要: Abstract Given a simple Lie algebra g and an element μ ∈ ⁎ , the corresponding shift of argument subalgebra S ( ) is Poisson commutative. In case where regular, this known to admit quantization, that is, it can be lifted commutative U . We show if type A, then property extends arbitrary μ, thus proving conjecture Feigin, Frenkel Toledano Laredo. The proof relies on explicit construction generators center affine vertex at critical level.