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 Blₚₜ(X) of X at one point also has semisimple quantum cohomology. In particular, the monodromy group of the quantum cohomology of Blₚₜ(X) is a reflectiongroup. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of Blₚₜ(X) depending only on the geometry of the exceptional divisor.