In Becker's String theory book Conformal transformation in D dimension is given by $$\delta x^{\mu}=a^{\mu}+\omega^{\mu}_{\hspace{5pt}\nu}x^{\nu}+\lambda x^{\mu} +b^{\mu}x^2-2x^{\mu}(b\cdot x)$$ While discussing $2$ dimensional infinitesimal conformal transformation BBS used the following transformation $$z\rightarrow z'=z-\epsilon_n z^{n+1} \hspace{5pt}n\in\mathbb{Z}$$ and it's complex conjugate. For $n=-1,0,1$ this infinitesimal transformation $\delta z=-\epsilon_n z^{n+1}$ can be fitted into the general equation. We have constant, linear, and quadratic terms and as the indices change we move over $z$ or $\bar{z}$. But for $n<-1$ and $n> 1$ this transformation doesn't fit the first general equation. Why is this so?
Although on the next page when discussing the $2$ dimensional transformation using generators we are told that $-1,0,1$ are special since all other generators can be calculated using the Virasoro algebra. I don't know if this idea has any relation (or is the answer) to my question?
