I believe the following statement is true:


Given a complex analytic map $f:\Delta\to V/G$, where $\Delta$ is a disc in $\mathbb{C}$, $V$ a finite dimensional complex vector space and $G$ a finite subgroup of $GL(V)$, then $f$ admits an analytic lift $\tilde f:\Delta'\to V$ up to a ramified cover. More precisely, there exists a ramified cover $r:\Delta'\to\Delta$ such that $f\circ r = \pi\circ \tilde f$ where $\pi:V\to V/G$ is the canonical projection.


I think I have a relatively elementary proof. 
However, this statement sounds very much like a "classical" result, but I have been unable to find a reference. Does anyone knows to whom I should attribute this result ?


Thanks a lot



Lifting analytic map
Salut Yann!


You can refer to the general notion of *fiber product*, for example. This is a construction that works in the complete generality. It might happen that in the situation you consider the fiber product will not be irreducible, (this happen when the preimage of $f(\Delta)$ in $V$ is not irreducible), then you just take one of the irreducible components of this fiber product. 


Here is a reference for fiber products : <http://planetmath.org/fibreproduct> .  

So according to the notations (I believe they are standard), this fiber product should be denoted as $\Delta\times \_{V/G} V$. 


