  Following the work of Kashiwara-Rouquier and Gan-Ginzburg, we define a family
of exact functors from category $\mathcal O$ for the rational Cherednik algebra
in type $A$ to representations of certain "coloured braid groups" and calculate
the dimensions of the representations thus obtained from standard modules. To
show that our constructions also make sense in a more general context, we also
briefly study the case of the rational Cherednik algebra corresponding to
complex reflection group $\mathbb Z/l\mathbb Z$.
