Recently in my class of lie algebra the profesor said the following statement
If we have $R\subset E$ (with $E$ The Euclidean space) an irreducible root system then $E$ is an irreducible representation of the Weyl group.
The thing is that he didn't proved it as he said it casually, but I wrote it on my notes. So, I wanted to prove it, but I tried and fail. Any help would be appreciated.