  Let g be a complex, semisimple Lie algebra. We prove the existence of a
quasi-Coxeter, quasitriangular quasibialgebra structure on the enveloping
algebra of g, which binds the quasi-Coxeter structure underlying the Casimir
connection of g and the quasitriangular quasibialgebra one underlying its KZ
equations. This implies in particular that the monodromy of the rational
Casimir connection of g is described by the quantum Weyl group operators of the
quantum group U_h(g).
