Reflection Vectors and Quantum Cohomology of Blowups

Let $X$ be a smooth projective variety with a semisimple quantum cohomology. It is known that the blowup ${\mathrm{Bl}}_{\mathrm{p}\mathrm{t}}(X)$ of $X$ at one point also has semisimple quantum cohomology. In particular, the monodromy group of the quantum cohomology of ${\mathrm{Bl}}_{\mathrm{p}\mathrm{t}}(X)$ is a reflectiongroup. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of ${\mathrm{Bl}}_{\mathrm{p}\mathrm{t}}(X)$ depending only on the geometry of the exceptional divisor.