  An approach, based on Jucys--Murphy elements, to the representation theory of
cyclotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke
algebra) of the set of the Jucys--Murphy elements is established. A basis of
the cyclotomic Hecke algebra is suggested; this basis is used to establish the
flatness of the deformation without use of the representation theory.
