For the generator $l_{n=-1}=-z^{n+1}\partial_z$ in 2 D conformal field theory, how did $\exp(sl_{-1})$ mapped $z$ to $z-s$?
$\exp(sl_{-1}) = \exp(s(-\partial_z)) = \exp(-s\partial_z)$ The claim was that this mapped $z\in\mathbb{C}$ to $z-s$.
I wasn't sure how the exponential map through the generator completed the transformation.