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In this paper we study Hurwitz spaces parameterizing coverings with special points and with monodromy group a Weyl group of type B d . We prove that such spaces are irreducible if k > 3d − 3. Here, k denotes the number of local monodromies that are reflections relative to long roots.doi:10.2298/fil1402275v fatcat:msjqdefzo5ftlcngqn3fr3e7vu