  A uniform parametrization for the irreducible spin representations of Weyl
groups in terms of nilpotent orbits is recently achieved by Ciubotaru (2011).
This paper is a generalization of this result to other real reflection groups.
Let $(V_0, R, V_0^{\vee}, R^{\vee})$ be a root system with the real reflection
group $W$. We define a special subset of points in $V_0^{\vee}$ which will be
called solvable points. Those solvable points, in the case $R$
crystallographic, correspond to the nilpotent orbits whose elements have a
solvable centralizer in the corresponding Lie algebra. Then a connection
between the irreducible spin representations of $W$ and those solvable points
in $V_0^{\vee}$ is established.
