Hurwitz spaces of Galois coverings of P^1 with Galois groups Weyl groups
  We prove the irreducibility of the Hurwitz spaces which parametrize Galois coverings of P^1 whose Galois group is an arbitrary Weyl group and the local monodromies are reflections. This generalizes a classical theorem due to Clebsch and Hurwitz. 
Vassil Kanev