Reflection vectors and quantum cohomology of blowups

Let $X$ be a smooth projective variety with a semi-simple quantum cohomology. It is known that the blow up $Bl(X)$ of $X$ at one point also has semi-simple quantum cohomology. In particular, the monodromy group of the quantum cohomology of $Bl(X)$ is a reflection group. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of $Bl(X)$ depending only on the geometry of the exceptional divisor.